## Educational Activity

### Course in Charge

- 2021, Liberal Arts Education Program1, 2Term, CalculusI
- 2021, Liberal Arts Education Program1, 4Term, CalculusII
- 2021, Liberal Arts Education Program1, 3Term, CalculusII
- 2021, Liberal Arts Education Program1, 3Term, CalculusII
- 2021, Undergraduate Education, 1Term, Mathematical Analysis
- 2021, Undergraduate Education, 3Term, Seminar in Mathematics I
- 2021, Undergraduate Education, 4Term, Seminar in Mathematics II
- 2021, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
- 2021, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
- 2021, Graduate Education (Master's Program) , First Semester, Seminar of Geometric and Algebraic Analysis
- 2021, Graduate Education (Master's Program) , Second Semester, Seminar of Geometric and Algebraic Analysis
- 2021, Graduate Education (Master's Program) , Academic Year, Geometric and Algebraic Analysis Seminar
- 2021, Graduate Education (Master's Program) , Academic Year, Geometric and Algebraic Analysis Seminar
- 2021, Graduate Education (Master's Program) , 1Term, Geometric and Algebraic Analysis A
- 2021, Graduate Education (Master's Program) , 2Term, Geometric and Algebraic Analysis B
- 2021, Graduate Education (Master's Program) , 3Term, Geometric and Algebraic Analysis C
- 2021, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
- 2021, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
- 2021, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
- 2021, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
- 2021, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

## Research Activities

### Academic Papers

- 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
- $L^2$-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
- 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
- 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
- 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
- N-soliton states of the Fermi-Pasta-Ulam lattices, SIAM Journal on Mathematical Analysis, 43(5), 2170-2210, 2011
- 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
- Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential, Kyoto Journal of Mathematics, 48(3), 471-497, 2008
- Instability of vortex solitons for 2D focusing NLS, Advances in Differential Equations, 12(3), 241-264, 20071201
- 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
- VORTEX SOLITONS FOR 2D FOCUSING NONLINEAR SCHRODINGER EQUATION, DIFFERENTIAL AND INTEGRAL EQUATIONS, 18(4), 431-450, 2005
- Asymptotic stability of solitary wave solutions to the regularized long-wave equation, Journal of Differential Equations, 200(2), 312-341, 20040610
- Weak interaction between solitary waves of the generalized KdV equations, SIAM Journal on Mathematical Analysis, 35(4), 1042-1080, 20040726
- Time decay of small solutions to quadratic nonlinear Schrödinger equations in 3D, Differential Integral Equations, 16(2), 159-179, 2003
- 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
- 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

### 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

- 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