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.

arXiv comment22 pages, no figure

References in corpus (2)

• Selection of the ground state for nonlinear Schroedinger equations
• Asymptotic stability of N-soliton states of NLS

Cited by in corpus (10)

• On asymptotic stability in energy space of ground states for Nonlinear Schrödinger equations
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• On asymptotic stability of standing waves of discrete Schrödinger equation in $\mathbb{Z}$
• A weighted estimate for two dimensional Schrodinger, matrix schrodinger and wave equations with resonance of first kind at zero energy
• A revision of "On asymptotic stability in energy space of ground states of NLS in 1D"
• A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
• On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D
• 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
• Stabilization of small solutions of discrete NLS with potential having two eigenvalues