## Existence of hylomorphic solitary waves in Klein-Gordon and in Klein-Gordon-Maxwell equations.(English)Zbl 1194.35343

The authors study solitary waves whose existence is related to the ratio energy/charge, and which are usually called hylomorphic. The class includes in particular the $$Q$$-balls which are spherically symmetric solutions of the nonlinear Klein-Gordon equation, as well as solitary waves and vortices appearing, by the same mechanism, in the nonlinear Schrödinger equation and the gauge theories. An abstract theorem is proved which allows to derive existence of hylomorphic solitary waves and vortices both for the nonlinear Klein-Gordon and for the nonlinear Klein-Gordon-Maxwell equations.

### MSC:

 35Q51 Soliton equations 35Q53 KdV equations (Korteweg-de Vries equations) 35Q55 NLS equations (nonlinear Schrödinger equations) 35C08 Soliton solutions 81V10 Electromagnetic interaction; quantum electrodynamics 81Q37 Quantum dots, waveguides, ratchets, etc.
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