On the soliton dynamics under slowly varying medium for Nonlinear Schrödinger equations
arXiv:1002.1295 · doi:10.1007/s00208-011-0706-8
Abstract
We consider the problem of the soliton propagation, in a slowly varying medium, for a generalized, variable-coefficients nonlinear Schrödinger equation. We prove existence and uniqueness of new soliton-like solutions for a large class of slowly varying media. Moreover, we describe for all time the behavior of this new generalized soliton solution.
49 pages, to appear in Math. Annalen
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