期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 75, 期 12, 页码 4398-4421出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2012.03.012
关键词
Lack of compactness; Orbital stability; Nonlinear Schrodinger equation; Lattice; Nonlinear Klein-Gordon equation; Solitary waves; Hylomorphic solitons; Vortices
Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time. A soliton is a solitary wave which exhibits some strong form of stability so that it has a particle-like behavior. In this paper, we prove a general, abstract theorem (Theorem 26) which allows to prove the existence of a class of solitons. Such solitons are suitable minimizers of a constrained functional and they are called hylomorphic solitons. Then we apply the abstract theory to problems related to the nonlinear Schrodinger equation (NSE) and to the nonlinear Klein-Gordon equation (NKG). (C) 2012 Elsevier Ltd. All rights reserved.
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