Sharp inelastic character of slowly varying NLS solitons

Details Sharp inelastic character of slowly varying NLS solitons Sharp inelastic character of slowly varying NLS solitons

2012-02-27

arxiv.org/abs/1202.5807v1

Mathematics

Analysis of PDEs

35 pp., submitted

Scientific paper

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.

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