Hylomorphic solitons in the nonlinear Klein-Gordon equation
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...
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Zusammenfassung: | 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 \emph{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. |
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DOI: | 10.48550/arxiv.0810.5079 |