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 H¹(, ), but not on all H¹(, ), and study its orbital stability.
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Fukuizumi et al. (2008) studied this question.
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