Mathematical Research Letters

Volume 16 (2009)

Number 3

A remark on soliton-potential interactions for nonlinear Schrödinger equations

Pages: 477 – 486

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n3.a8

Author

Galina Perelman (Ecole Polytechnique)

Abstract

We study the interaction of small amplitude solitons with a repulsive potential $V$ for the nonlinear Schrödinger equation $i\psi_t=-\psi_{xx}+V(x)\psi+F(|\psi|^2)\psi$. We show that in the case where the nonlinearity $F(\xi)$ is $L_2$ critical at zero, the incoming soliton is splitted by $V$ into two outgoing waves that radiate to zero as $t\rightarrow +\infty$.

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