Graduate School Human and Environmental Studies/Mathematical and Information Sciences
Undergraduate School Mathematical and Information Sciences (Division of Cognitive and Information Sciences)
Other Affiliation
Email hayashi.masayuki.3m AT
Personal Page Website
Until 2023, the undergraduate school had five divisions. 'Division' provided above refers to the faculty member's former affiliation.
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Research areas Partial Differential Equations
Keywords Nonlinear Dispersive Equations, Schrödinger Equations, Solitary Waves, Solitons
Themes Nonlinear partial differential equations appear in various situations as model equations that describe physical phenomena. My main research interest is a class of nonlinear partial differential equations called dispersive equations, and I am interested in elucidating mathematical structure inherent in these equations. The field of mathematics involved is wide-ranging and has many mathematically interesting subjects. Recently, I have been focusing on research investigating the dynamics around solitary waves (solitons).
Major publications Well-posedness for a generalized derivative nonlinear Schrödinger equation, J. Differential
Equations 261 (2016), 5424–5445. (with T. Ozawa)

A sufficient condition for global existence of solutions to a generalized derivative nonlinear
Schrödinger equation, Anal. PDE 10 (2017), 1149–1167. (with N. Fukaya and T. Inui)

Potential well theory for the derivative nonlinear Schrödinger equation, Anal. PDE 14
(2021), 909–944.

Instability of algebraic standing waves for nonlinear Schrödinger equations with double
power nonlinearities, Trans. Amer. Math. Soc. 374 (2021), 1421–1447. (with N. Fukaya)

Stability of algebraic solitons for nonlinear Schrödinger equations of derivative type: variational approach, Ann. Henri Poincaré 23 (2022), 4249–4277.

Traveling waves for a nonlinear Schrödinger system with quadratic interaction, Math. Ann. 388 (2024), 1357–1378. (with N. Fukaya and T. Inui)
Professional societies/Research and synergic activities The Mathematical Society of Japan
Teaching Areas
  • Undergraduate courses Seminar in Mathematics and Informatics
    Introduction to Mathematical and Information Sciences
  • Graduate courses (Master's program) Fundamentals for Transdisciplinary Research 1
    Seminar on Mathematics of Phenomena 3A, 3B
  • Graduate courses (Doctor's program)
  • Undergraduate courses open to all departments Calculus with Exercises A, B
人間・環境学研究科パンフレット 総合人間学部パンフレット