On the soliton dynamics under slowly varying medium for Nonlinear Schrödinger equations

Details On the soliton dynamics under slowly varying medium for Nonlinear Schrödinger equations On the soliton dynamics under slowly varying medium for Nonlinear Schrödinger equations

2010-02-05

arxiv.org/abs/1002.1295v4

Mathematics

Analysis of PDEs

49 pages, to appear in Math. Annalen

Scientific paper

10.1007/s00208-011-0706-8

We consider the problem of the soliton propagation, in a slowly varying
medium, for a generalized, variable-coefficients nonlinear Schr\"odinger
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.

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