Updated on 2025/05/03

写真a

 
Kawamoto Masaki
 
Organization
Scheduled update Associate Professor
Position
Associate Professor
External link

Degree

  • 博士 (理学) ( 神戸大学 )

Research Interests

  • Strichartz estimate

  • Schr\"{o}dinger equations

  • electromagnetic field

  • Scattering theory

  • Non-selfadjoint operator

Research Areas

  • Natural Science / Mathematical analysis

Research History

  • Okayama University   The Research Institute for Interdisciplinary Science   Assistant Professor

    2024.4

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  • Ehime University   理工学研究科   Associate Professor

    2022.10 - 2024.3

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  • Ehime University   Graduate School of Science and Engineering   Lecturer

    2019.10 - 2022.9

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  • Université de Bordeaux   Researcher

    2019.4 - 2019.7

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  • Tokyo University of Science   Department of Mathematics, Faculty of Science   Research Associate

    2017.4 - 2019.9

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  • Kobe University   Department of Mathematics, faculty of science   Researcher

    2015.4 - 2017.3

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  • Kobe University   Graduate School of Science Division of Mathematics

    2012.4 - 2015.3

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  • Kobe University   Graduate School of Science Division of Mathematics

    2010.4 - 2012.3

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  • Kobe University   Faculty of Science Department of Mathematics

    2006.3 - 2010.4

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Professional Memberships

 

Papers

  • Modified scattering operator for nonlinear Schrödinger equations with time-decaying harmonic potentials Reviewed

    Masaki Kawamoto, Hayato Miyazaki

    Nonlinear Analysis   256   113778 - 113778   2025.7

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    Language：English   Publisher：Elsevier BV  

    DOI： 10.1016/j.na.2025.113778

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  • Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance Reviewed

    Masaki Kawamoto, Satoshi Masaki, Hayato Miyazaki

    Mathematische Annalen   392 ( 1 )   1051 - 1097   2025.2

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    Authorship：Corresponding author   Language：English   Publisher：Springer Science and Business Media LLC  

    Abstract

    In this paper, we consider the nonlinear Schrödinger equation (NLS) with a general homogeneous nonlinearity in dimensions up to three. We assume that the degree (i.e., power) of the nonlinearity is such that the equation is mass-subcritical and short-range. We establish global well-posedness (GWP) and scattering for small data in the standard weighted space for a class of homogeneous nonlinearities, including non-gauge-invariant ones. Additionally, we include the case where the degree is less than or equal to the Strauss exponent. When the nonlinearity is not gauge-invariant, the standard Duhamel formulation fails to work effectively in the weighted Sobolev space; for instance, the Duhamel term may not be well-defined as a Bochner integral. To address this issue, we introduce an alternative formulation that allows us to establish GWP and scattering, even in the presence of poor time continuity of the Duhamel term.

    DOI： 10.1007/s00208-025-03121-w

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    Other Link： https://link.springer.com/article/10.1007/s00208-025-03121-w/fulltext.html

  • Modified scattering for nonlinear Schrödinger equations with long-range potentials Reviewed

    Masaki Kawamoto, Haruya Mizutani

    Transactions of the American Mathematical Society   2025.2

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Mathematical Society (AMS)  

    <p>We study the final state problem for the nonlinear Schrödinger equation with a critical long-range nonlinearity and a long-range linear potential. Given a prescribed asymptotic profile which is different from the free evolution, we construct a unique global solution scattering to the profile. In particular, the existence of the modified wave operators is obtained for sufficiently localized small scattering data. The class of potential includes a repulsive long-range potential with a short-range perturbation, especially the positive Coulomb potential in two and three space dimensions. The asymptotic profile is constructed by combining Yafaev’s type linear modifier associated with the long-range part of the potential and the nonlinear modifier introduced by Ozawa. Finally, we also show that one can replace Yafaev’s type modifier by Dollard’s type modifier under a slightly stronger decay assumption on the long-range potential. This is the first positive result on the modified scattering for the nonlinear Schrödinger equation in the case when both of the nonlinear term and the linear potential are of long-range type.</p>

    DOI： 10.1090/tran/9369

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    Other Link： https://www.ams.org/tran/0000-000-00/S0002-9947-2025-09369-3/S0002-9947-2025-09369-3.pdf

  • Nonexistence of wave operators via strong propagation estimates for Schrödinger operators with sub-quadratic repulsive potentials Reviewed

    Atsuhide Ishida, Masaki Kawamoto

    Journal of Mathematical Physics   64 ( 12 )   2023.12

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：AIP Publishing  

    Sub-quadratic repulsive potentials accelerate quantum particles and can relax the decay rate in the x of the external potentials V that guarantee the existence of the quantum wave operators. In the case where the sub-quadratic potential is −|x|α with 0 &amp;lt; α &amp;lt; 2 and the external potential satisfies |V(x)| ≤ C(1 + |x|)−(1−α/2)−ɛ with ɛ &amp;gt; 0, Bony et al. [J. Math. Pures Appl. 84, 509–579 (2005)] determined the existence and completeness of the wave operators, and Itakura [J. Math. Phys. 62, 061504 (2021)] then obtained their results using stationary scattering theory for more generalized external potentials. Based on their results, we naturally expect the following. If the decay power of the external potential V is less than −(1 − α/2), V is included in the short-range class. If the decay power is greater than or equal to −(1 − α/2), V is included in the long-range class. In this study, we first prove the new propagation estimates for the time propagator that can be applied to scattering theory. Second, we prove that the wave operators do not exist if the power is greater than or equal to −(1 − α/2) and that the threshold expectation of −(1 − α/2) is true using the new propagation estimates.

    DOI： 10.1063/5.0164176

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  • Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials Reviewed

    Masaki Kawamoto, Hayato Miyazaki

    Journal of Differential Equations   365   127 - 167   2023.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jde.2023.04.009

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  • Asymptotic behavior of solutions to a dissipative nonlinear Schrödinger equation with time-dependent harmonic potentials Reviewed

    Masaki Kawamoto, Takuya Sato

    Journal of Differential Equations   345   418 - 446   2023.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jde.2022.11.034

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  • Strichartz estimates for quadratic repulsive potentials Reviewed

    Masaki Kawamoto, Taisuke Yoneyama

    Partial Differential Equations and Applications   3 ( 15 )   2022.1

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  • Asymptotic behavior for nonlinear Schr\"{o}dinger equations with critical time-decaying harmonic potential Reviewed

    Masaki Kawamoto

    Journal of Differential Equations   303 ( 5 )   253 - 267   2021.12

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

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  • Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators Reviewed

    Masaki Kawamoto

    Journal of Mathematical Analysis and Applications   503 ( 1 )   125292 - 125292   2021.11

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.jmaa.2021.125292

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  • Absence of embedded eigenvalues for Hamiltonian with crossed magnetic and electric fields Reviewed

    Mouez Dimassi, Masaki Kawamoto, Vesselin Petkov

    Reviews in Mathematical Physics   33 ( 6 )   2150020   2021

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  • Critical scattering in a time-dependent harmonic oscillator Reviewed

    Atsuhide Ishida, Masaki Kawamoto

    Journal of Mathematical Analysis and Applications   492 ( 2 )   2020.12

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  • Strichartz Estimates for Schrödinger Operators with Square Potential with Time-Dependent Coefficients Reviewed

    Masaki Kawamoto

    Differential Equations and Dynamical Systems   31 ( 4 )   827 - 845   2020.7

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s12591-020-00537-5

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    Other Link： https://link.springer.com/article/10.1007/s12591-020-00537-5/fulltext.html

  • L^2 properties for linearized KdV equation around small solutions Reviewed

    Masaki Kawamoto

    SUT Journal of Mathematics   56 ( 1 )   1 - 19   2020.6

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  • Existence and non-existence of wave operators for time-decaying harmonic oscillators Reviewed

    Atsuhide Ishida, Masaki Kawamoto

    Reports on Mathematical Physics   85 ( 3 )   335 - 350   2020.6

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    Controlled time-decaying harmonic potentials decelerate the velocity of charged particles; however, the particles are never trapped by the harmonic potentials. This physical phenomenon changes the threshold between the short-range and long-range classes of the potential through physical wave operators. We herein report that the threshold is 1/(1 − λ) for some 0 ≤ λ < 1/2, as determined using the mass of the particle and a coefficient of the harmonic potential.

    DOI： 10.1016/S0034-4877(20)30040-9

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  • Singularity for solutions of linearized KdV equations Reviewed

    Keiichi Kato, Masaki Kawamoto, Koichiro Nanbu

    Journal of Mathematical Physics   61 ( 5 )   2020.5

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  • Asymptotic behavior of solutions to nonlinear Schrödinger equations with time-dependent harmonic potentials Reviewed

    Masaki Kawamoto, Ryo Muramatsu

    Journal of Evolution Equations   21   699 - 723   2020

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    Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

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  • Strichartz estimates for Schr\"{o}dinger operators with unbounded potentials Reviewed

    Masaki Kawamoto

    RIMSKokyurokuBessatsu (to appear)   2020

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    Language：English   Publishing type：Research paper (international conference proceedings)  

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  • Mourre theory for time-periodic magnetic field Reviewed

    Masaki Kawamoto

    Journal of Functional Analysis   277   1 - 30   2019.7

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  • Klein-Gordon equations with homogeneous time-dependent electric fields Reviewed

    Masaki Kawamoto

    ANNAL DELL'UNIVERSITA'DI FERRARA   64 ( 2 )   389 - 406   2017.10

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  • Strichartz estimates for harmonic potential with time-decaying coefficients Reviewed

    Masaki Kawamoto, Taisuke Yoneyama

    Journal of evolution equations   18 ( 1 )   127 - 142   2017.4

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  • EXPONENTIAL DECAY PROPERTY FOR EIGENFUNCTIONS OF LANDAU-STARK HAMILTONIAN Reviewed

    Masaki Kawamoto

    REPORTS ON MATHEMATICAL PHYSICS   77 ( 1 )   129 - 140   2016.2

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：PERGAMON-ELSEVIER SCIENCE LTD  

    In this paper, we study the exponential decay property for eigenfuctions of a perturbed Landau-Stark Hamiltonian. As a result, we prove this property for long-range Coulomb-type perturbations.

    DOI： 10.1016/S0034-4877(16)30009-X

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  • Quantum Scattering in a Periodically Pulsed Magnetic Field Reviewed

    Tadayoshi Adachi, Masaki Kawamoto

    ANNALES HENRI POINCARE   17 ( 9 )   2409 - 2438   2016.1

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER BASEL AG  

    In this paper, we study the quantum dynamics of a charged particle in the plane in the presence of a periodically pulsed magnetic field perpendicular to the plane. We show that by controlling the cycle when the magnetic field is switched on and off appropriately, the result of the asymptotic completeness of wave operators can be obtained under the assumption that the potential V satisfies the decaying condition for some .

    DOI： 10.1007/s00023-016-0457-x

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  • Avron-Herbst Type Formula in Crossed Constant Magnetic and Time-Dependent Electric Fields Reviewed

    Tadayoshi Adachi, Masaki Kawamoto

    LETTERS IN MATHEMATICAL PHYSICS   102 ( 1 )   65 - 90   2012.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    In this paper, we give an Avron-Herbst type formula for the propagator generated by the free Hamiltonian with crossed constant magnetic and time-dependent electric fields. As an application of the formula, we give a result of the existence of the wave operators under some appropriate conditions on the time-dependent electric field and the potential. Finally, in the case where the electric field is time-independent, we consider the problem of the asymptotic completeness of the wave operators.

    DOI： 10.1007/s11005-012-0555-8

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MISC

  • Modified scattering for the cubic nonlinear Schrödinger equation with long-range potentials in one space dimension

    Masaki Kawamoto, Haruya Mizutani

    arXiv:2412.16872   2024.12

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  • On Schrödinger equation with square and inverse-square potentials

    Atsuhide Ishida, Masaki Kawamoto

    arXiv:2404.04756   2024.4

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    Authorship：Lead author  

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  • On quantum system with time-periodic magnetic fields

    Masaki Kawamoto

    RIMS Kokyuroku   2021

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  • Asymptotic completeness of wave operators for Schrödinger operators with time-periodic magnetic fields

    Masaki Kawamoto

    arXiv:2105.06116   2021

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    Authorship：Lead author   Language：English   Publishing type：Internal/External technical report, pre-print, etc.  

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  • Energy Stableness for Schrödinger Operators with Time-Dependent Potentials

    Masaki Kawamoto

    arXiv:1910.11551   2019.10

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  • High-energy smoothing estimates for selfadjoint operators

    Masaki Kawamoto

    arXiv:1811.02853   2018.11

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  • Scattering in a periodically pulsed magnetic field

    Masaki Kawamoto

    RIMS Kokyuroku 2023 Spectral and Scattering Theory and Related Topics   2017.4

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    Language：English   Publishing type：Article, review, commentary, editorial, etc. (international conference proceedings)  

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  • Quantum scattering for time-decaying harmonic oscillators

    Masaki Kawamoto

    arXiv: 1704.03714   2017.4

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    Language：English   Publishing type：Internal/External technical report, pre-print, etc.  

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Presentations

  • Asymptotic behavior for nonlinear Schrodinger equation with critical time-dependent harmonic potential Invited

    Masaki Kawamoto

    2022.6.1 

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    Event date： 2022.6.1 - 2022.6.3

    Presentation type：Oral presentation (general)  

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  • 線形化 KdV 方程式の諸問題について Invited

    川本昌紀

    線形および非線形分散型方程式の研究の進展  2021.5.20 

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    Event date： 2021.5.17 - 2021.5.20

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 時間減衰する調和ポテンシャルをもつ非線形 Schr\"{o}dinger 方程式 の解の漸近挙動について Invited

    川本昌紀

    オンラインワークショップ「分散型方程式と実解析」  2020.12.9 

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    Event date： 2020.12.9 - 2020.12.10

    Presentation type：Oral presentation (general)  

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  • Magnetic-Stark Hamiltonian の固有値問題について Invited

    川本昌紀

    第９回信州関数解析シンポジウム  2020.10.26 

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    Event date： 2020.10.26 - 2020.10.28

    Presentation type：Oral presentation (general)  

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  • Modified scattering for the nonlinear Schr\"odinger equations with long-range potentials in 1D Invited

    Masaki Kawamoto

    2025.5.23 

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  • Global well-posedness for nonlinear Schrödinger equations below the Strauss exponent Invited

    Masaki Kawamoto

    Himeji Conference on Partial Differential Equations  2025.3.5 

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    Language：English  

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  • Modified scattering for nonlinear Schrödinger equations with long-range potentials Invited

    川本昌紀

    岡山大学数学科 談話会  2024.9.9 

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    Presentation type：Oral presentation (general)  

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  • Modified scattering for nonlinear Schrödinger equations with long-range potentials

    Masaki Kawamoto, Haruya Mizutani

    2024.9.5 

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    Presentation type：Oral presentation (general)  

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  • Modified scattering for nonlinear Schrödinger equations with long-range potentials Invited

    2024.8.30 

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  • Strauss 指数を越えない 2 次元非線形シュレ ディンガー方程式の時間大域的適切性について Invited

    川本昌紀

    第77回 南大阪応用数学セミナー  2024.6.29 

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    Presentation type：Oral presentation (general)  

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  • Strauss 指数を越えない 2 次元非線形シュレ ディンガー方程式の時間大域的適切性について Invited

    川本昌紀

    第8回 神楽坂非線形波動研究会  2024.6.19 

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    Presentation type：Oral presentation (general)  

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  • Schrödinger equation with square and inverse square potentials Invited

    Masaki Kawamoto

    Workshop on dispersive PDE  2024.4.26 

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    Language：English   Presentation type：Oral presentation (general)  

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  • Modified scattering for nonlinear Schrödinger equations with long-range potentials

    2024.4.19 

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  • 時間減衰磁場中の非線形修正散乱作用素の構成について

    川本昌紀

    愛媛大学 数学談話会  2024.3.22 

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  • 時間減衰する調和振動子を持つ非線形シュレディンガー方程式の修正散 乱作用素について

    川本昌紀, 宮崎隼人

    日本数学会2024年度春季分科会  2024.3.19 

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  • 時間減衰調和振動子付き非線形シュレディンガー方程式に対する 散乱作用素の構成について Invited

    川本昌紀

    Workshop on nonlinear wave equations and related topics in Kobe  2023.11.13 

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  • Modified scattering for nonlinear Schrödinger equations with long-range potentials Invited

    Masaki Kawamoto

    Online Seminars on PDEs and Harmonic Analysis  2023.10.13 

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  • Modified scattering for nonlinear Schr\"odinger equations with long-range potentials Invited

    Masaki Kawamoto

    2023.10.6 

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  • Nonexistence of wave operators for sub-quadratic repulsive potential

    Atsuhide Ishida, Masaki Kawamoto

    2023.9.20 

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  • Fractional Laplacian の時間減衰評価と非線形長距離散乱について Invited

    川本昌紀

    非線型分散型・双曲型偏微分方程式の解の長時間挙動  2023.9.12 

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  • Modified scattering for nonlinear Schrodinger equations with long-range potentials Invited

    Masaki Kawamoto

    Harmonic Analysis and Nonlinear Partial Differential Equations  2023.7.3 

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    Language：English   Presentation type：Oral presentation (general)  

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  • Nonexistence of wave operators for sub-quadratic repulsive potentials Invited

    Masaki Kwamoto

    2023.4.8 

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  • D(H) ⊂ D(i[H,A]^0)) でない場合の Mourre理論やsmoothingについて

    川本昌紀

    第４回スペクトル・散乱若手勉強会  2023.3.11 

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  • Long-range scattering for nonlinear Schrodinger equation with time-decaying harmonic potential Invited

    Masaki Kawamoto

    2023.2.18 

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  • Nonexistence of wave operators for sub-quadratic repulsive potentials Invited

    Masaki Kawamoto

    2023.1.12 

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  • Long-range scattering for nonlinear Schrodinger equation with potential Invited

    Masaki Kawamoto

    2023.1.9 

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  • Nonexistence of wave operators and propagation estimates for sub-quadratic repulsive potentials Invited

    Masaki KAWAMOTO

    RIMS conference "Spectral and scattering theory and related topics"  2022.12.1 

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    Language：English   Presentation type：Oral presentation (general)  

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  • 長距離型の非線形項と線形ポテンシャルを持つ非線形シュレディンガー方程式の解の漸近系について

    川本昌紀

    第２回 香川における偏微分方程式研究会  2022.11.25 

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    Presentation type：Oral presentation (general)  

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  • Magnetic-Stark ハミルトニアンの埋蔵固有値の非存在について Invited

    川本昌紀

    大阪大学微分方程式セミナー  2022.11.18 

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  • 時間減衰する調和振動子を持つ臨界斉次型非線形シュレディンガー方程式における長距離散乱について

    宮崎隼人, 川本昌紀

    日本数学会秋季学会  2022.9.15 

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  • 臨界係数を持つ時間減衰調和振動子に対する波動作用素の存在・非存在について

    川本昌紀, 石田敦英

    日本数学会秋季学会  2022.9.13 

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  • ポテンシャル付きNLSの諸問題について

    川本昌紀

    香川における偏微分方程式研究会  2021.11.27 

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  • 2次元 Magnetic-Stark ハミルトニアンの固有値問題について Invited

    川本昌紀

    作用素論セミナ－  2021.11.19 

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  • 時間減衰する調和振動子に対する波動作用素の存在・非存在について

    川本昌紀, 石田敦英

    日本数学会2021年度秋季総合分科会  2021.9.14 

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  • 時間減衰する調和ポテンシャルを持つシュレーディンガー方程式の散乱について Invited

    川本昌紀

    Workshop on Analysis in Kagurazaka 2020  2020.1.24 

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  • Scattering theory for time-periodic magnetic fields Invited

    川本昌紀

    微分方程式の総合的研究  2019.12.22 

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    Language：English   Presentation type：Oral presentation (general)  

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  • Mourre theory for time-periodic magnetic fields Invited

    Masaki Kawamoto

    Spectral and scattering theory and related topics  2019.12.3 

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  • Mourre theory for time-periodic magnetic fields

    川本昌紀

    第２９回数理物理と微分方程式  2019.11.2 

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  • 時間周期磁場中のシュレーディンガー方程式について Invited

    川本昌紀

    愛媛解析セミナー  2019.10.18 

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  • 時間周期磁場中のシュレーディンガー方程式について Invited

    川本昌紀

    大阪大学微分方程式セミナー  2019.10.11 

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  • ある磁場中シュレーディンガー作用素に対する散乱理論について Invited

    川本昌紀

    箱根における偏微分方程式研究会  2019.9.28 

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  • Mourre theory for time-periodic magnetic fields

    川本昌紀

    日本数学会 秋季学会  2019.9.17 

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  • Mourre theory for time-periodic magnetic fields Invited

    Masaki Kawamoto

    Seminaire de Physique Mathematics-EDP  2019.5.21 

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    Presentation type：Oral presentation (general)  

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  • Strichartz estimates for Schrödinger operators with time-decaying harmonic oscillator Invited

    川本昌紀

    NED in Kumamoto  2019.1.12 

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  • Quantum scattering for time-decaying harmonic oscillators Invited

    川本昌紀

    シュレーディンガー方程式の数理とその周辺  2019.1.7 

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  • Quantum scattering for time-decaying harmonic oscillators Invited

    川本昌紀

    第229回広島数理解析セミナー  2018.11.30 

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    Presentation type：Oral presentation (general)  

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  • Klein-Gordon equations with time-dependent electric fields

    川本昌紀

    第28回数理物理と微分方程式  2018.11.3 

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    Presentation type：Oral presentation (general)  

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  • Strichartz estimates for Schrödinger operators with time-decaying harmonic oscillator Invited

    川本昌紀

    Okayama Workshop on Partial Differential Equation  2018.10.20 

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    Presentation type：Oral presentation (general)  

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  • 線形化KdV方程式の解のL^2安定性について Invited

    川本昌紀

    箱根における偏微分方程式研究会  2018.9.29 

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    Presentation type：Oral presentation (general)  

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  • Klein–Gordon equations with homogeneous time-dependent electric fields

    川本昌紀

    日本数学会 秋季学会  2018.9.24 

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  • 線形化KdV方程式の解のL^2安定性について

    川本昌紀

    夏の作用素論シンポジウム  2018.9.2 

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    Presentation type：Oral presentation (general)  

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  • Strichartz estimates for Schrödinger operators with unbounded potentials Invited

    Masaki Kawamoto

    Regularity, singularity and asymptotic behavior of solutions to partial differential equations with conservation law  2018.5.30 

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    Presentation type：Oral presentation (general)  

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  • 定電場中のクライン-ゴルドン方程式について Invited

    川本昌紀

    函館偏微分方程式研究集会  2017.10.8 

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  • ホール効果と固有値問題 Invited

    川本昌紀

    箱根における偏微分方程式研究会  2017.9.30 

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  • Scattering theory for time-decaying harmonic oscillators Invited

    川本昌紀

    信州偏微分方程式研究集会  2017.6.16 

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  • 一様電場内を運動する相対論的粒子に対する散乱理論 Invited

    川本昌紀

    神楽坂解析セミナー  2017.4.22 

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  • 一様電場内を運動する相対論的粒子に対する散乱理論 Invited

    川本昌紀

    神戸大学解析セミナー  2017.2.7 

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  • Quantum scattering in time-depending electromagnetic fields Invited

    Masaki Kawamoto

    Workshop on Analysis in Kagurazaka 2017  2017.1.27 

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  • Scattering in electromagnetic fields Invited

    Masaki Kawamoto

    Symposium on Spectral and Scattering Theory in Matsumoto  2017.1.9 

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  • Scattering in a periodically pulsed magnetic field Invited

    Masaki Kawamoto

    The 14 th linear and nonlinear waves  2016.11.4 

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  • Magnetic-Stark Hamiltonian に対するスペクトル理論

    川本昌紀

    夏の作用素論シンポジウム  2016.9.4 

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  • Klein-Gordon system with electric fields Invited

    Masaki Kawamoto

    Lectures on Semi-Classical Analysis  2016.7.6 

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  • Scattering in a periodically pulsed magnetic field Invited

    川本昌紀

    RIMS 研究集会 Spectral and Scattering Theory and Related Topics  2016.1.22 

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  • パルス磁場上での散乱 Invited

    川本昌紀

    熊本大学応用解析セミナー  2015.12.5 

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  • 時間に依存した電磁場と荷電粒子の散乱

    川本昌紀

    第26回数理物理と微分方程式  2015.11.1 

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  • パルス磁場上の散乱 Invited

    川本昌紀

    スペクトル理論セミナー  2015.7.18 

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  • パルス磁場上の散乱 Invited

    川本昌紀

    第1回彦根解析セミナー  2015.6.6 

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  • 外場中のクラインーゴルドン方程式の解の存在と伝播評価

    川本昌紀

    第11回 数学総合若手研究集会  2015.3.4 

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  • 時間に依存する一様電場と定磁場内における散乱問題 Invited

    川本昌紀

    作用素論セミナー  2014.10 

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  • 電磁場中のシュレーディンガー作用素に対するスペクトル・散乱理論

    川本昌紀

    第36回発展方程式若手セミナー  2014.8.31 

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  • 電磁場中の粒子に対する散乱理論

    川本昌紀

    第10回 数学総合若手研究集会  2013.3.3 

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  • 時間に依存したハミルト二アンに対する散乱理論

    川本昌紀

    第10回 城崎新人セミナー  2013.2.20 

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  • 時間に依存する一様電場と定磁場内における散乱問題 Invited

    川本昌紀

    スペクトル・散乱 松山シンポジウム  2013.1 

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  • 時間に依存する一様電場と定磁場内における散乱問題 Invited

    川本昌紀

    スペクトル理論セミナー  2012.10.20 

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  • Exponential decay property for eigenfunctions of Landau-Stark Hamiltonian Invited International conference

    Masaki Kawamoto

    Conference on Quantum World 2018 

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    Presentation type：Oral presentation (general)  

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  • Quantum scattering theory in time-dependent magnetic fields I, II Invited

    Masaki Kawamoto

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    Presentation type：Oral presentation (invited, special)  

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  • Quantum sattering in a periodically pulsed magnetic field Invited International conference

    Masaki Kawamoto

    Symposium on Spectral and Scattering Theory 

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    Presentation type：Oral presentation (general)  

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  • 時間周期パルス磁場に対する散乱理論 Invited

    川本 昌紀

    日本数学会 秋季特別講演 

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    Presentation type：Oral presentation (invited, special)  

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Research Projects

  • 電磁場中の非線形シュレディンガー方程式の修正散乱についての多角的研究

    Grant number：24K06796  2024.04 - 2028.03

    日本学術振興会  科学研究費助成事業  基盤研究(C)

    川本 昌紀、米山泰祐

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    Authorship：Principal investigator 

    Grant amount：\4550000 （ Direct expense: \3500000 、 Indirect expense：\1050000 ）

    researchmap

  • Spectral and scattering theory for Schr\"{o}dinger equations in magnetic fields

    Grant number：20K14328  2020.04 - 2024.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Early-Career Scientists  Grant-in-Aid for Early-Career Scientists

    Masaki Kawamoto

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    Grant amount：\4160000 （ Direct expense: \3200000 、 Indirect expense：\960000 ）

    2021年度は3本の論文が国際誌に掲載され、現在1本を投稿中であり、5本の論文を作成している。
    昨年度より進めていた非線形への応用であるが、まずは時間減衰磁場中の非線形散乱を考察し、終値問題を完成させた。この結果により非線形散乱が磁場項が付いた場合も考察できる事が分かり、現在はこの結果の非線形項をより一般のものにして同様の研究が出来るかを宮崎隼人氏(香川大学)と考察している。この論文は J. Math. Anal. Appl. に掲載された。また非線形項も時間減衰磁場もクリティカルの場合における非線形シュレーディンガー方程式の初期値問題及び漸近挙動の解析を行なった。この論文は J. Diff. Eqn. に掲載された。この結果により時間減衰磁場から対数型の非線形項が自然に導かれることが分かり、これは数学的にも物理学的にも興味深い結果であり、今後はより精密な評価を考察していく。
    今後の研究として、以前から継続して行っている宮崎氏(香川大学)との共同研究に加え、水谷治哉氏(大阪大学)、佐藤拓也氏(東北大学)との共同研究を行っており、ポテンシャル項付きのシュレーディンガー方程式についての研究を精力的に進めている。
    線形問題に関しては、斥力ポテンシャルの付いたシュレーディンガー方程式に対するストリッカーツの評価式についての論文が partial diff. eqn. and appl. に掲載され、この研究は時間周期磁場中の非線形シュレーディンガー方程式への応用が期待される。今後はこの結果の応用を考察していく。
    線形問題の今後の研究に関しては現在、石田敦英氏(東京理科大学)と斥力ポテンシャルの付いた問題の伝播評価について研究を進めている。

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  • 時間に依存した電磁場中の Schr\"{o}dinger 方程式の解の漸近挙動の解析

    2018.08 - 2019.03

    東京理科大学  研究戦略中期計画推進費 

    川本 昌紀

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    Authorship：Principal investigator  Grant type：Competitive

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Class subject in charge

  • Glance at Mathematical Science B （2024academic year） Third semester  - 金5～6

  • Seminar in Mathematical Analysis （2024academic year） Year-round  - その他

  • Probability　and　Statistics （2024academic year） 3rd and 4th semester  - 火5～6

  • Probability　and　Statistics a （2024academic year） Third semester  - 火5～6

  • Probability　and　Statistics b （2024academic year） Fourth semester  - 火5～6

  • Stochastic Differential Equations （2024academic year） Late  - その他

  • Linear Algebra 1 （2024academic year） Third semester  - 木5～6

  • Linear Algebra 2 （2024academic year） Fourth semester  - 木5～6

  • Excercises in Analysis （2024academic year） 1st and 2nd semester  - 火3～4

  • Analysis I （2024academic year） 1st and 2nd semester  - 火1～2

  • Analysis Ia （2024academic year） 1st semester  - 火1～2

  • Analysis Ib （2024academic year） Second semester  - 火1～2

  • Advanced Practice in Functional Analysis 1 （2024academic year） Prophase  - その他

  • Advanced Practice in Functional Analysis 2 （2024academic year） Late  - その他

  • Advanced Practice in Functional Analysis 3 （2024academic year） Prophase  - その他

  • Advanced Practice in Functional Analysis 4 （2024academic year） Late  - その他

  • Advanced Course on Functional Analysis （2024academic year） Late  - 月1～2

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