TETSU MIZUMACHI

Last Updated :2021/04/06

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Professor
E-mail
tetsumhiroshima-u.ac.jp

Basic Information

Academic Degrees

  • The University of Tokyo
  • The University of Tokyo

Educational Activity

Course in Charge

  1. 2021, Liberal Arts Education Program1, 2Term, CalculusI
  2. 2021, Liberal Arts Education Program1, 4Term, CalculusII
  3. 2021, Liberal Arts Education Program1, 3Term, CalculusII
  4. 2021, Liberal Arts Education Program1, 3Term, CalculusII
  5. 2021, Undergraduate Education, 1Term, Mathematical Analysis
  6. 2021, Undergraduate Education, 3Term, Seminar in Mathematics I
  7. 2021, Undergraduate Education, 4Term, Seminar in Mathematics II
  8. 2021, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  9. 2021, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  10. 2021, Graduate Education (Master's Program) , First Semester, Seminar of Geometric and Algebraic Analysis
  11. 2021, Graduate Education (Master's Program) , Second Semester, Seminar of Geometric and Algebraic Analysis
  12. 2021, Graduate Education (Master's Program) , Academic Year, Geometric and Algebraic Analysis Seminar
  13. 2021, Graduate Education (Master's Program) , Academic Year, Geometric and Algebraic Analysis Seminar
  14. 2021, Graduate Education (Master's Program) , 1Term, Geometric and Algebraic Analysis A
  15. 2021, Graduate Education (Master's Program) , 2Term, Geometric and Algebraic Analysis B
  16. 2021, Graduate Education (Master's Program) , 3Term, Geometric and Algebraic Analysis C
  17. 2021, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
  18. 2021, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
  19. 2021, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
  20. 2021, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
  21. 2021, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

Research Activities

Academic Papers

  1. The Phase Shift of Line Solitons for the KP-II Equation, Fields Institute Communications, 83, 433-495, 20190101
  2. Stability of line solitons for the KP-II equation in ℝ2. II, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148(1), 149-198, 20180201
  3. Asymptotic linear stability of Benney-Luke line solitary waves in 2D, Nonlinearity, 30(9), 3419-3465, 20170807
  4. $L^2$-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
  5. Asymptotic stability of solitary waves in the benney-luke model of water waves, Differential and Integral Equations, 26(3-4), 253-301, 20130301
  6. Asymptotic Stability of N-Solitary Waves of the FPU Lattices, Archive for Rational Mechanics and Analysis, 207(2), 393-457, 20130201
  7. 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
  8. Bäcklund transformation and L 2-stability of NLS solitons, International Mathematics Research Notices, 2012(9), 2034-2067, 20120507
  9. Stability of the line soliton of the KP-II equation under periodic transverse perturbations, Mathematische Annalen, 352(3), 659-690, 20120301
  10. N-soliton states of the Fermi-Pasta-Ulam lattices, SIAM Journal on Mathematical Analysis, 43(5), 2170-2210, 2011
  11. Description of the inelastic collision of two solitary waves for the BBM equation, Archive for Rational Mechanics and Analysis, 196(2), 517-574, 20100501
  12. Asymptotic stability of lattice solitons in the energy space, Communications in Mathematical Physics, 288(1), 125-144, 20090501
  13. On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations, Communications in Mathematical Physics, 284(1), 51-77, 20081101
  14. Existence of periodic traveling wave solutions for the Ostrovsky equation, Mathematical Methods in the Applied Sciences, 31(14), 1646-1652, 20080925
  15. Asymptotic stability of Toda lattice solitons, Nonlinearity, 21(9), 2099-2111, 20080901
  16. Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential, Kyoto Journal of Mathematics, 48(3), 471-497, 2008
  17. Instability of vortex solitons for 2D focusing NLS, Advances in Differential Equations, 12(3), 241-264, 20071201
  18. Asymptotic stability of small solitons for 2D nonlinear Schrödinger equations with potential, Kyoto Journal of Mathematics, 47(3), 599-620, 20070101
  19. A remark on linearly unstable standing wave solutions to NLS, Nonlinear Analysis, Theory, Methods and Applications, 64(4), 657-676, 20060215
  20. Instability of bound states for 2D nonlinear Schrödinger equations, Discrete and Continuous Dynamical Systems, 13(2), 413-428, 20050101
  21. VORTEX SOLITONS FOR 2D FOCUSING NONLINEAR SCHRODINGER EQUATION, DIFFERENTIAL AND INTEGRAL EQUATIONS, 18(4), 431-450, 2005
  22. Asymptotic stability of solitary wave solutions to the regularized long-wave equation, Journal of Differential Equations, 200(2), 312-341, 20040610
  23. Weak interaction between solitary waves of the generalized KdV equations, SIAM Journal on Mathematical Analysis, 35(4), 1042-1080, 20040726
  24. Time decay of small solutions to quadratic nonlinear Schrödinger equations in 3D, Differential Integral Equations, 16(2), 159-179, 2003
  25. 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
  26. Time decay of solutions to degenerate Kirchhoff type equation, Nonlinear Analysis, Theory, Methods and Applications, 33(3), 235-252, 19980101
  27. Decay properties of solutions to degenerate wave equations with dissipative terms, Advances in Differential Equations, 2(4), 573-592, 19971201
  28. 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

  1. 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

  1. 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