Sharp inelastic character of slowly varying NLS solitons

Abstract

We consider soliton-like solutions of a variable coefficients, subcritical nonlinear Schrodinger equation (NLS). In a previous result, we proved the existence of a pure, global-in-time, generalized soliton with prescribed asymptotic as t tends to -infinity. In addition, we described the corresponding dynamics for all time, up to a small error term. In this paper we prove that the soliton is never pure as t tends to infinity. Indeed, we give a precise sharp lower bound on the defect induced by the potential on the soliton. This result shows the existence of nontrivial dispersive effects acting on generalized solitons of slowly varying NLS equations.

Some remarks added and a few typos corrected

References in corpus (6)

• Solitary Wave Dynamics in an External Potential
• Fast soliton scattering by delta impurities
• Asymptotic stability of N-soliton states of NLS
• Soliton splitting by external delta potentials
• On the inelastic 2-soliton collision for gKdV equations with general nonlinearity
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Cited by in corpus (2)

• A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
• On weak interaction between a ground state and a non-trapping potential