Transverse instability of the line solitary water-waves

TL;DR

This paper proves that line solitary water waves are unstable when subjected to transverse disturbances, highlighting a fundamental limitation in their stability properties.

Contribution

It establishes the linear and nonlinear instability of line solitary water waves against transverse perturbations, a significant theoretical advancement.

Findings

Proves linear instability of water waves with transverse perturbations

Demonstrates nonlinear instability of these waves

Provides mathematical framework for stability analysis

Abstract

We prove the linear and nonlinear instability of the water line solitary waves with respect to transverse perturbations.