## Basic Information

### Academic Degrees

- The University of Tokyo
- The University of Tokyo

### Research Fields

- Mathematical and physical sciences;Mathematics;Mathematical analysis

## Educational Activity

### Course in Charge

- 2024, Liberal Arts Education Program1, 4Term, CalculusII
- 2024, Liberal Arts Education Program1, 3Term, CalculusII
- 2024, Undergraduate Education, 1Term, Mathematical Analysis
- 2024, Undergraduate Education, 3Term, Seminar in Mathematics I
- 2024, Undergraduate Education, 4Term, Seminar in Mathematics II
- 2024, Graduate Education (Master's Program) , 2Term, Mathematical Omnibus
- 2024, Graduate Education (Master's Program) , Academic Year, Geometric and Algebraic Analysis Seminar
- 2024, Graduate Education (Master's Program) , 1Term, Geometric and Algebraic Analysis A
- 2024, Graduate Education (Master's Program) , 3Term, Geometric and Algebraic Analysis B
- 2024, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
- 2024, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
- 2024, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
- 2024, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
- 2024, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
- 2024, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

## Research Activities

### Academic Papers

- VORTEX SOLITONS FOR 2D FOCUSING NONLINEAR SCHRODINGER EQUATION, DIFFERENTIAL AND INTEGRAL EQUATIONS, 18(4), 431-450, 2005
- $L^2$-stability of solitary waves for the KdV equation via Pego and Weinstein's method (Harmonic Analysis and Nonlinear Partial Differential Equations), RIMS Kokyuroku Bessatsu, 49, 33-63, 201406
- Time decay of small solutions to quadratic nonlinear Schrödinger equations in 3D, Differential Integral Equations, 16(2), 159-179, 2003
- The Phase Shift of Line Solitons for the KP-II Equation, Fields Institute Communications, 83, 433-495, 20190101
- Stability of line solitons for the KP-II equation in ℝ
^{2}. II, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148(1), 149-198, 20180201 - Asymptotic linear stability of Benney-Luke line solitary waves in 2D, Nonlinearity, 30(9), 3419-3465, 20170807
- Asymptotic stability of solitary waves in the benney-luke model of water waves, Differential and Integral Equations, 26(3-4), 253-301, 20130301
- Asymptotic Stability of N-Solitary Waves of the FPU Lattices, Archive for Rational Mechanics and Analysis, 207(2), 393-457, 20130201
- Bäcklund transformation and L
^{2}-stability of NLS solitons, International Mathematics Research Notices, 2012(9), 2034-2067, 20120507 - Stability of the line soliton of the KP-II equation under periodic transverse perturbations, Mathematische Annalen, 352(3), 659-690, 20120301
- Description of the inelastic collision of two solitary waves for the BBM equation, Archive for Rational Mechanics and Analysis, 196(2), 517-574, 20100501
- Asymptotic stability of lattice solitons in the energy space, Communications in Mathematical Physics, 288(1), 125-144, 20090501
- On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations, Communications in Mathematical Physics, 284(1), 51-77, 20081101
- Existence of periodic traveling wave solutions for the Ostrovsky equation, Mathematical Methods in the Applied Sciences, 31(14), 1646-1652, 20080925
- Asymptotic stability of Toda lattice solitons, Nonlinearity, 21(9), 2099-2111, 20080901
- Instability of vortex solitons for 2D focusing NLS, Advances in Differential Equations, 12(3), 241-264, 20071201
- Asymptotic stability of solitary wave solutions to the regularized long-wave equation, Journal of Differential Equations, 200(2), 312-341, 20040610
- Asymptotic stability of small solitons for 2D nonlinear Schrödinger equations with potential, Kyoto Journal of Mathematics, 47(3), 599-620, 20070101
- A remark on linearly unstable standing wave solutions to NLS, Nonlinear Analysis, Theory, Methods and Applications, 64(4), 657-676, 20060215
- Instability of bound states for 2D nonlinear Schrödinger equations, Discrete and Continuous Dynamical Systems, 13(2), 413-428, 20050101
- Weak interaction between solitary waves of the generalized KdV equations, SIAM Journal on Mathematical Analysis, 35(4), 1042-1080, 20040726
- Large time asymptotics of solutions around solitary waves to the generalized Korteweg-de Vries equations, SIAM Journal on Mathematical Analysis, 32(5), 1050-1080, 20010101
- Time decay of solutions to degenerate Kirchhoff type equation, Nonlinear Analysis, Theory, Methods and Applications, 33(3), 235-252, 19980101
- Decay properties of solutions to degenerate wave equations with dissipative terms, Advances in Differential Equations, 2(4), 573-592, 19971201
- On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger equation, Discrete and Continuous Dynamical Systems - Series S, 5(5), 971-987, 20121001
- N-soliton states of the Fermi-Pasta-Ulam lattices, SIAM Journal on Mathematical Analysis, 43(5), 2170-2210, 2011
- Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential, Kyoto Journal of Mathematics, 48(3), 471-497, 2008
- The asymptotic behavior of solutions to the Kirchhoff equation with a viscous damping term, Journal of Dynamics and Differential Equations, 9(2), 211-247, 19971201
- STABILITY OF BENNEY-LUKE LINE SOLITARY WAVES IN 2 DIMENSIONS, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 52(5), 4238-4283, 2020

### Publications such as books

- 2015, Stability of line solitons for the KP-II equation in $\mathbb{R^2}$, We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as x goes to infinity We find that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward at y equals plus or minus infinity. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms., Scholarly Book, 英語, Tetsu Mizumachi, 978-1-4704-1424-5 (print); 978-1-4704-2613-2 (online), 102

### Invited Lecture, Oral Presentation, Poster Presentation

- Stability of line solitons for the KP-II equation, Tetsu Mizumachi, Singularity formation and long-time behavior in dispersive PDEs, 2016/03/15, Without Invitation, English, Roland Donninger (U Bonn), Herbert Koch (U Bonn), University of Bonn
- Stability of line solitons for the KP-II equation, Tetsu Mizumachi, Nonlinear Waves 2016: May Conference, 2016/05/26, With Invitation, English, Frank MERLE (University of Cergy-Pontoise & IHES) Pierre RAPHAËL (University Nice Sophia-Antipolis) Nikolay TZVETKOV (University of Cergy-Pontoise), IHES, France
- Stability of line solitons for the KP-II equation, Nonlinear Wave and Dispersive Equations, Kyoto 2016, 2016/09/06, With Invitation, English, Reika Fukuizumi (Tohoku University) Nobu Kishimoto (Kyoto University) Kenji Nakanishi (Osaka University) Masahito Ohta (Tokyo University of Science) Hideo Takaoka (Hokkaido University) Kotaro Tsugawa (Nagoya University)
- On stability of line solitons for the KP-II equation, 2015/07/08, With Invitation, English
- Stability of line solitons for the KP-II equation, The 33rd Kyushu Symposium on Partial Differential Equations, 2016/01/29, With Invitation, English
- On stability of line solitons of the KP-II equation, Tetsu Mizumachi, International Workshop on Fundamental Problems in Mathematical and Theoretical Physics, 2015/09/28, With Invitation, English, Hiromichi Nakazato, Tohru Ozawa, Kazuya Yuasa
- Stability of line solitons for the KP-II equation, 2016/10/29, With Invitation, Japanese
- Stability of line solitons, 2015/07/29, With Invitation, English
- Asymptotic Linear Stability of Benney-Luke line solitary waves in 2D, Tetsu Mizumachi, Yusuke Shimabukuro, Workshop on Inverse Scattering and Dispersive PDEs in Two Space Dimensions, 2017/08, With Invitation, English, Toronto, Canada
- Asymptotic linear stability of Benney-Luke line solitary waves in 2D, Tetsu Mizumachi, Tosio Kato Centennial Conference, 2017/09, With Invitation, English, Tokyo
- On the phase shift of line solitary waves for the KP-II equation, Tetsu Mizumachi, Workshop on Nonlinear Water Waves, 2018/05, With Invitation, English, Takanori Hino (Yokohama National University) Tatsuo Iguchi (Keio University) Taro Kakinuma (Kagoshima University) Takeshi Kataoka (Kobe University) Ken-ichi Maruno (Waseda University) Tetsu Mizumachi (Hiroshima University) Sunao Murashige (Ibaraki University) Yasuhiro Ohta (Kobe University), Kyoto
- Stability of line solitary waves for some long wave models, Tetsu Mizumachi, Yusuke Shimabukuro, Workshop on Nonlinear Dispersive Partial Differential Equations and Inverse Scattering, 2019/05, With Invitation, Japanese, Peter Miller - University of Michigan Peter Perry - University of Kentucky Jean-Claude Saut - Université Paris-Sud Catherine Sulem - University of Toronto, Fields Institute, Canada