DCDS
Stability of standing waves for a nonlinear Schrödinger equation wdelta potentialith a repulsive Dirac
Reika Fukuizumi Louis Jeanjean
Discrete & Continuous Dynamical Systems - A 2008, 21(1): 121-136 doi: 10.3934/dcds.2008.21.121
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
DCDS
Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential
Reika Fukuizumi
Discrete & Continuous Dynamical Systems - A 2001, 7(3): 525-544 doi: 10.3934/dcds.2001.7.525
In this paper, we study the stability and the instability of standing waves for the nonlinear Schrödinger equation with harmonic potential. We prove the existence of stable or unstable standing waves under certain conditions on the power of nonlinearity and the frequency of wave.
keywords: harmonic potential Nonlinear Schrödinger equation standing wave orbital stability.

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