On the Davey-Stewartson hierarchy: construction by two scalar pseudo-differential operators and compatibility for infinite many flows

TL;DR

This paper presents a direct algorithm to construct the Davey-Stewartson hierarchy using two scalar pseudo-differential operators, linking its symmetries to integrable surface deformations in four-dimensional space.

Contribution

It introduces a novel method for constructing the DS hierarchy through scalar pseudo-differential operators, enhancing understanding of its integrable structure.

Findings

Explicit construction of DS hierarchy via pseudo-differential operators

Connection between DS symmetries and surface deformations in 4D

Framework for analyzing infinite symmetries of integrable systems

Abstract

The infinite many symmetries of Davey-Stewartson (DS) system are closely connected to the integrable deformations of surfaces in a four-dimensional space. In this paper, we give a direct algorithm to construct the expression of the DS hierarchy by two scalar pseudo-differential operators involving partial derivatives.