## Journals

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### Open Access Journals

DCDS

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

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.

## Year of publication

## Related Authors

## Related Keywords

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