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Solitons for the nonlinear Klein-Gordon equation. (English) Zbl 1200.35248

Summary: We study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the ratio energy/charge of a function, which turns out to be a useful approach for many field equations.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
47J35 Nonlinear evolution equations
35C08 Soliton solutions
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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