Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

TL;DR

This paper investigates the transverse spectral stability of generalized solitary waves in a fifth-order KP model, revealing their instability due to the transverse instability of their periodic tails through detailed spectral analysis.

Contribution

It provides the first detailed spectral analysis showing the transverse instability of generalized solitary waves in a fifth-order KP equation.

Findings

Generalized solitary waves are transversely spectrally unstable.

The instability is caused by the transverse instability of the periodic tails.

Spectral analysis of linear operators underpins the instability proof.

Abstract

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.