Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac

Reika Fukuizumi; Louis Jeanjean

doi:10.3934/dcds.2008.21.121

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2008, Volume 21, Issue 1: 121-136. Doi: 10.3934/dcds.2008.21.121

This issue Previous Article On the behavior of solutions to Schrödinger equations with dipole type potentials near the singularity Next Article Schrödinger equations with a spatially decaying nonlinearity: Existence and stability of standing waves

Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac

Reika Fukuizumi^1, and
Louis Jeanjean^2,

1.
Department of Mathematics, Hokkaido University, Sapporo 060-0810
2.
Equipe de Mathématiques (UMR CNRS 6623), Université de Franche-Comté, 16 Route de Gray, 25030 Besançon

Received: December 2006

Revised: March 2007

Published online: February 2008

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Abstract

We consider a stationary nonlinear Schröodinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We prove that it is a minimizer of the associated energy on the subspace of even functions of $H^1(\R, \C)$, but not on all $H^1(\R, \C)$, and study its orbital stability.

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Mathematics Subject Classification: Primary: 35B35, 35Q55; Secondary: 35Q51, 35A15.

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