Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations

TL;DR

This paper demonstrates the existence of a family of periodic solitons in the elliptic-elliptic focusing Davey-Stewartson equations, revealing their structure and stability properties.

Contribution

It introduces a new family of periodic solitons with specific spatial profiles and analyzes their linear stability, expanding understanding of solutions in these equations.

Findings

Existence of periodic solitons with line soliton profile in longitudinal direction.

Line soliton is linearly unstable to transverse perturbations.

Use of dynamical systems methods to establish soliton existence.

Abstract

We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which have the profile of the line soliton in the longitudinal spatial direction and are periodic in the transverse spatial direction, is established using dynamical systems arguments. We also show that the line soliton is linearly unstable with respect to perturbations in the transverse direction.