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Abstract: Roughly speaking a solitary wave is a solution of a field equation whoseenergy travels as a localised packet and which preserves this localisation intime. A soliton is a solitary wave which exhibits some strong form of stabilityso that it has a particle-like behaviour. In this paper we show a new mechanismwhich might produce solitary waves and solitons for a large class of equations,such as the nonlinear Klein-Gordon equation. We show that the existence ofthese kind of solitons, that we have called \emph{hylomorphic} solitons,depends on a suitable energy-charge ratio. We show a variational method thatallows to prove the existence of hylomorphic solitons and that turns out to bevery useful for numerical applications. Moreover we introduce some classes ofnonlinearities which admit hylomorphic solitons of different shapes and withdifferent relations between charge, energy and frequency.



Author: J. Bellazzini, V. Benci, C. Bonanno, E. Sinibaldi

Source: https://arxiv.org/







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