Hylomorphic solitons on lattices

TL;DR

This paper proves the existence of hylomorphic solitons on lattices, including Q-balls and vortices, by establishing an abstract theorem applicable to various nonlinear equations on lattice structures.

Contribution

It introduces a general existence theorem for hylomorphic solitons on lattices, encompassing known solutions like Q-balls and extending to new lattice-based models.

Findings

Existence of hylomorphic solitons on lattices proven.

The theorem applies to nonlinear Klein-Gordon and Schrödinger equations.

Includes solutions such as Q-balls and vortices.

Abstract

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.