A simple criterion of transverse linear instability for solitary waves

TL;DR

This paper introduces a new, simple criterion for determining the transverse linear instability of solitary waves, providing a theoretical tool applicable to various physical models.

Contribution

It presents an abstract instability criterion for eigenvalue problems and demonstrates its application to establish the transverse instability of solitary waves in different physical contexts.

Findings

Established a new criterion for instability analysis.

Proved transverse linear instability for specific solitary wave examples.

Provided a theoretical framework applicable to mathematical physics models.

Abstract

We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various examples from mathematical physics.