On stability of small solitons of the 1--D NLS with a trapping delta potential
Abstract
We consider a Nonlinear Schr\"odinger Equation with a very general non linear term and with a trapping δ potential on the line. We then discuss the asymptotic behavior of all its small solutions, generalizing a recent result by Masaki et al. We give also a result of dispersion in the case of defocusing equations with a non--trapping delta potential.
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