Zakharov-Shabat system and hyperbolic pseudoanalytic function theory

TL;DR

This paper explores the relationship between the Zakharov-Shabat system and hyperbolic pseudoanalytic function theory, demonstrating how the inverse problem method connects to hyperbolic Vekua equations and enabling explicit construction of formal powers.

Contribution

It establishes a novel link between the Zakharov-Shabat system and hyperbolic Vekua equations, allowing explicit generation of formal powers in hyperbolic pseudoanalytic function theory.

Findings

Zakharov-Shabat system is related to hyperbolic Vekua equations

Explicit construction of formal powers is possible

Enhances understanding of inverse problem methods in hyperbolic contexts

Abstract

In [1] a hyperbolic analogue of pseudoanalytic function theory was developed. In the present contribution we show that one of the central objects of the inverse problem method the Zakharov-Shabat system is closely related to a hyperbolic Vekua equation for which among other results a generating sequence and hence a complete system of formal powers can be constructed explicitly.