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On the solitary wave dynamics, under slowly varying medium, for nonlinear Schrödinger equations

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Abstract

We consider the problem of a solitary wave propagation, in a slowly varying medium, for a variable-coefficients nonlinear Schrödinger equation. We prove global existence and uniqueness of solitary wave solutions for a large class of slowly varying media. Moreover, we describe for all time the behavior of these solutions, which include refracted and reflected solitary waves, depending on the initial energy.

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  1. Departamento de Ingeniería Matemática, Universidad de Chile, Blanco Encalada 2120, piso 5, Casilla 170-3, Correo 3, Santiago, Chile

    Claudio Muñoz

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  1. Claudio Muñoz
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Muñoz, C. On the solitary wave dynamics, under slowly varying medium, for nonlinear Schrödinger equations. Math. Ann. 353, 867–943 (2012). https://doi.org/10.1007/s00208-011-0706-8

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  • DOI: https://doi.org/10.1007/s00208-011-0706-8

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