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Hylomorphic solitons in the nonlinear Klein-Gordon equation

Bellazzini, Jacopo and Bonanno, Claudio and Sinibaldi, Edoardo and Benci, Vieri (2009) Hylomorphic solitons in the nonlinear Klein-Gordon equation. Dynamics of Partial Differential Equations, Vol. 6 (4), p. 311-334. ISSN 1548-159X. eISSN 2163-7873. Article.

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Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localised packet and which preserves this localisation in time. A soliton is a solitary wave which exhibits some strong form of stability so that it has a particle-like behaviour. In this paper we show a new mechanism which might produce solitary waves and solitons for a large class of equations, such as the nonlinear Klein-Gordon equation. We show that the existence of these kind of solitons, that we have called hylomorphic solitons, depends on a suitable energy/charge ratio. We show a variational method that allows to prove the existence of hylomorphic solitons and that turns out to be very useful for numerical applications. Moreover we introduce some classes of nonlinearities which admit hylomorphic solitons of different shapes and with different relations between charge, energy and frequency.

Item Type:Article
ID Code:6927
Uncontrolled Keywords:Hylomorphic solitons, nonlinear Klein-Gordon equation
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Divisions:001 Università di Sassari > 01 Dipartimenti > Scienze botaniche, ecologiche e geologiche
Publisher:International Press
Deposited On:10 Jan 2012 09:34

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