A minimization method and applications to the study of solitons

Details A minimization method and applications to the study of solitons A minimization method and applications to the study of solitons

2011-11-08

arxiv.org/abs/1111.1888v1

Mathematics

Analysis of PDEs

arXiv admin note: substantial text overlap with arXiv:1103.1131

Scientific paper

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 ex istence 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 Schr\"odinger equation (NSE) and to the nonlinear Klein-Gordon equation (NKG).

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