Solitons in Schr\"odinger-Maxwell equations

TL;DR

This paper develops an abstract existence theory for solitons and applies it to the Schr"odinger-Maxwell equations, demonstrating the existence of stable, finite energy solutions.

Contribution

It introduces a general framework for soliton existence and applies it specifically to the nonlinear Schr"odinger-Maxwell equations.

Findings

Established conditions for soliton existence in NSM

Proved stability of certain finite energy solutions

Extended abstract soliton theory to coupled equations

Abstract

In this paper we study the Nonlinear Schr\"odinger-Maxwell equations (NSM). We are interested to analyse the existence of solitons, namely of finite energy solutions which exhibit stability properties. This paper is divided in two parts. In the first, we give an abstract definition of soliton and we develope an abstract existence theory. In the second, we apply this theory to NSM.