Transverse nonlinear instability of Euler-Korteweg solitons

TL;DR

This paper demonstrates that solitary wave solutions of the 2D Euler-Korteweg model become nonlinearly unstable when disturbed transversely, highlighting a critical aspect of their stability behavior.

Contribution

It provides the first analysis of transverse nonlinear instability for Euler-Korteweg solitons, revealing their vulnerability to specific perturbations.

Findings

Solitary waves are nonlinearly unstable under transverse perturbations.

The instability occurs in the 2D Euler-Korteweg model for capillary fluids.

This instability impacts the understanding of wave stability in fluid dynamics.

Abstract

We show that solitary waves for the 2D Euler-Korteweg model for capillary fluids display nonlinear instability when subjected to transverse perturbations.