{ "id": "1002.1295", "version": "v4", "published": "2010-02-05T18:41:04.000Z", "updated": "2011-08-09T18:28:54.000Z", "title": "On the soliton dynamics under slowly varying medium for Nonlinear Schrödinger equations", "authors": [ "Claudio Muñoz" ], "comment": "49 pages, to appear in Math. Annalen", "doi": "10.1007/s00208-011-0706-8", "categories": [ "math.AP", "math-ph", "math.MP" ], "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.", "revisions": [ { "version": "v4", "updated": "2011-08-09T18:28:54.000Z" } ], "analyses": { "subjects": [ "35Q51", "35Q53" ], "keywords": [ "slowly varying medium", "nonlinear schrödinger equations", "soliton dynamics", "soliton propagation", "generalized soliton solution" ], "tags": [ "journal article" ], "note": { "typesetting": "TeX", "pages": 49, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2010arXiv1002.1295M" } } }