General Zakharov-Shabat equations without Lax operators

TL;DR

This paper demonstrates that Zakharov-Shabat equations can recover Lax operators through variable transformations in the KP and modified KP hierarchies, offering a new perspective on integrable systems without relying on Lax operators.

Contribution

It shows that Zakharov-Shabat equations alone can determine Lax operators in certain hierarchies, removing the need for predefined Lax operators.

Findings

Zakharov-Shabat equations recover Lax operators via variable change

Applicable to KP and modified KP hierarchies

Provides a new approach to integrable systems

Abstract

The operators in the Zakharov-Shabat equations of integrable hierarchies are usually defined from the Lax operators. In this article it is shown that the Zakharov-Shabat equations themselves recover the Lax operators under suitable change of independent variables in the case of the KP hierarchy and the modified KP hierarchy (in the matrix formulation).