Negative Times of the Davey-Stewartson Integrable Hierarchy

TL;DR

This paper explores the extension of the Davey-Stewartson hierarchy to include negative time evolutions, deriving new Lax pairs and integrable equations to expand the hierarchy's framework.

Contribution

It introduces negative time evolutions in the Davey-Stewartson hierarchy, providing new Lax pairs and integrable equations not previously considered.

Findings

Negative time evolutions are compatible with the Davey-Stewartson hierarchy.

New Lax pairs corresponding to negative time flows are derived.

Extended hierarchy includes additional integrable equations.

Abstract

We use example of the Davey-Stewartson hierarchy to show that in addition to the standard equations given by Lax operator and evolutions of times with positive numbers, one can consider time evolutions with negative numbers and the same Lax operator. We derive corresponding Lax pairs and integrable equations.