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January  2008, 21(1): 121-136. doi: 10.3934/dcds.2008.21.121

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, Japan
2. 

Equipe de Mathématiques (UMR CNRS 6623), Université de Franche-Comté, 16 Route de Gray, 25030 Besançon

Received  December 2006 Revised  March 2007 Published  February 2008

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.
Keywords: variational methods., Dirac delta, standing waves, stability, nonlinear Schrödinger equation.
Mathematics Subject Classification: Primary: 35B35, 35Q55; Secondary: 35Q51, 35A1.
Citation: Reika Fukuizumi, Louis Jeanjean. Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac. Discrete & Continuous Dynamical Systems, 2008, 21 (1) : 121-136. doi: 10.3934/dcds.2008.21.121
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