On Classification of Integrable Davey-Stewartson Type Equations

TL;DR

This paper classifies integrable Davey-Stewartson type equations by identifying systems generated by polynomial dispersionless Lax pairs and employs hydrodynamic reductions to recover these systems and their Lax pairs, revealing some potentially new systems.

Contribution

It provides a systematic classification of integrable Davey-Stewartson type equations using polynomial dispersionless Lax pairs and hydrodynamic reductions, including the discovery of new systems.

Findings

List of potentially deformable dispersionless systems

Recovery of integrable systems and their Lax pairs

Identification of some new integrable systems

Abstract

This paper is devoted to the classification of integrable Davey-Stewartson type equations. A list of potentially deformable dispersionless systems is obtained through the requirement that such systems must be generated by a polynomial dispersionless Lax pair. A perturbative approach based on the method of hydrodynamic reductions is employed to recover the integrable systems along with their Lax pairs. Some of the found systems seem to be new.