On stability of small solitons of the 1--D NLS with a trapping delta potential

Abstract

We consider a Nonlinear Schrödinger Equation with a very general non linear term and with a trapping $\delta$ 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.

References in corpus (3)

• Fast soliton scattering by delta impurities
• Soliton splitting by external delta potentials
• Asymptotic stability of ground states in 2D nonlinear Schrödinger equation including subcritical cases