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- Tetsu Mizumachi
- SIAM J. Math. Analysis
- 2001

- Tetsu Mizumachi
- SIAM J. Math. Analysis
- 2003

In this paper we study the large time behavior of two decoupled solitary waves of the generalized KdV equations ut + (uxx + f(u))x = 0, where f(u) = |u|p−1u/p (3 ≤ p < 5). We prove that if the speeds… (More)

- Tetsu Mizumachi
- 2006

We study instability of a vortex soliton eφω,m(r) to iut + ∆u + |u| u = 0, for x ∈ R, t > 0, where n = 2, m ∈ N and (r, θ) are polar coordinates in R. Grillakis [11] proved that every radially… (More)

AbstractWe consider nonlinear Schrödinger equations
$$iu_t +\Delta u +\beta (|u|^2)u=0\, ,\, \text{for} (t,x)\in \mathbb{R}\times \mathbb{R}^d,$$ where d ≥ 3 and β is smooth. We prove that symmetric… (More)

- Tetsu Mizumachi
- 2004

- Tetsu Mizumachi
- 2008

We prove the nonlinear stability of the KdV solitary waves considered as solutions of the KP-II equation, with respect to periodic transverse perturbations. Our proof uses a Miura transform which… (More)

- Tetsu Mizumachi
- 2005

- Tetsu Mizumachi
- 2009

Orbital and asymptotic stability for 1-soliton solutions of the Toda lattice equations as well as for small solitary waves of the FPU lattice equations are established in the energy space. Unlike… (More)

We establish an asymptotic stability result for Toda lattice soliton solutions, by making use of a linearized Bäcklund transformation whose domain has codimension one. Combining a linear stability… (More)