arXiv:1111.1888 Abstract | arXiv Analytics

arXiv:1111.1888 [math.AP]Abstract References Reviews Resources

A minimization method and applications to the study of solitons

Published 2011-11-08Version 1

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).

Comments: arXiv admin note: substantial text overlap with arXiv:1103.1131

Categories: math.AP, math-ph, math.MP

Subjects: 47J30, 35J50, 35Q55, 35Q51, 37K45

Keywords: minimization method, applications, solitary wave, nonlinear klein-gordon equation, energy travels

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