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Mathematics  2010 

On the soliton dynamics under slowly varying medium for Nonlinear Schr?dinger equations

DOI: 10.1007/s00208-011-0706-8

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Abstract:

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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