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

Abstract

We consider asymptotic stability of a small solitary wave to supercritical 2-dimensional nonlinear Schrödinger equations $$i{u}_t+\Delta u=Vu\pm |u{|}^{p-1}u\text{for (x,t)∈R2×R,}$$ in the energy class.

22 pages, no figure

References in corpus (1)

• Asymptotic stability of N-soliton states of NLS

Cited by in corpus (6)

• On asymptotic stability of standing waves of discrete Schrödinger equation in $\mathbb{Z}$
• A revision of "On asymptotic stability in energy space of ground states of NLS in 1D"
• On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D
• A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
• On asymptotic stability of ground states of NLS with a finite bands periodic potential in 1D
• Scattering theory in homogeneous Sobolev spaces for Schrödinger and wave equations with rough potentials