An abstract theorem on the existence of hylomorphic solitons

TL;DR

This paper presents an abstract theorem that provides a general framework for establishing the existence of hylomorphic solitons in various PDE-based dynamical systems, along with illustrative applications.

Contribution

The paper introduces a novel abstract theorem that facilitates the proof of soliton existence across diverse dynamical systems described by PDEs.

Findings

Theorem applicable to multiple PDE systems for soliton existence

Method demonstrated with specific dynamical systems

Framework simplifies soliton existence proofs

Abstract

In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to prove the existence of solitons in some dynamical systems.