Hylomorphic solitons on lattices

Details Hylomorphic solitons on lattices Hylomorphic solitons on lattices

2010-03-08

arxiv.org/abs/1003.1616v1

Mathematics

Analysis of PDEs

28 pages

Scientific paper

This paper is devoted to prove the existence of solitons on lattices. We are interested in solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions of the nonlinear Klein-Gordon equation, as well as solitary waves and vortices which occur, by the same mechanism, in the nonlinear Schroedinger equation and in gauge theories. In this paper we prove an abstract existence theorem which applies to many situations already considered in the literature and also to the nonlinear Schroedinger (and Klein-Gordon) equations defined on a lattice.

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