Tetsu Mizumachi

On Asymptotic Stability in Energy Space of Ground States for Nonlinear Schrödinger Equations

AbstractWe consider nonlinear Schrödinger equations

Weak Interaction between Solitary Waves of the Generalized KdV Equations

iu_t +\Delta u +\beta (|u|^2)u=0\, ,\, \text{for} (t,x)\in \mathbb{R}\times \mathbb{R}^d,

Large Time Asymptotics of Solutions Around Solitary Waves to the Generalized Korteweg--de Vries Equations

where d ≥ 3 and β is smooth. We prove that symmetric finite energy solutions close to orbitally stable ground states converge to a sum of a ground state and a dispersive wave as t → ∞ assuming the so called the Fermi Golden Rule (FGR) hypothesis. We improve the “sign condition” required in a recent paper by Gang Zhou and I.M.Sigal.

N-soliton states of the fermi-pasta-ulam lattices

We establish an asymptotic stability result for Toda lattice soliton solutions, by making use of a linearized Backlund transformation whose domain has codimension one. Combining a linear stability result with a general theory of nonlinear stability by Friesecke and Pego for solitary waves in lattice equations, we conclude that all solitons in the Toda lattice are asymptotically stable in an exponentially weighted norm. In addition, we determine the complete spectrum of an operator naturally associated with the Floquet theory for these lattice solitons.

Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential

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

Stability of the line soliton of the KP-II equation under periodic transverse perturbations

f(u)=|u|^{p-1}u/p

Asymptotic stability of small solitons for 2D Nonlinear Schrödinger equations with potential

(

Asymptotic Stability of Lattice Solitons in the Energy Space

3\le p < 5