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
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