A remark on soliton-potential interactions for nonlinear Schrödinger equations

• Autores: Galina Perelman
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 16, Nº 2-3, 2009, págs. 477-486
• Idioma: inglés
• DOI: 10.4310/mrl.2009.v16.n3.a8
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the interaction of small amplitude solitons with a repulsive potential $V$ for the nonlinear Schr\"odinger 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 $t\rightarrow +\infty$.