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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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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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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    Language：English  

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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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    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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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 ）

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  • 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

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