Hylomorphic solitons for the generalized KdV equation

TL;DR

This paper proves the existence of hylomorphic solitons in the generalized KdV equation, demonstrating a new class of stable solitary waves linked to energy-charge relations.

Contribution

It introduces the concept of hylomorphic solitons and establishes their existence within the generalized KdV framework, highlighting a novel stability mechanism.

Findings

Existence of hylomorphic solitons in the generalized KdV equation

Stability due to energy and hylenic charge relation

New class of stable solitary waves

Abstract

In this paper we prove the existence of hylomorphic solitons in the generalized KdV equation. A soliton is called hylomorphic if it is a solitary wave whose stability is due to a particular relation between energy and another integral of motion which we call hylenic charge.