A remark on soliton-potential interactions for nonlinear Schrödinger equations

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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Published 1 January 2009