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 Schrödinger equation (NSE) and to the nonlinear Klein–Gordon equation (NKG).

A minimization method and application to the study of solitons

FORTUNATO, Donato
2012

Abstract

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 Schrödinger equation (NSE) and to the nonlinear Klein–Gordon equation (NKG).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/29753
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