On the Caudrey-Beals-Coifman System and the Gauge Group Action

TL;DR

This paper explores the mathematical properties and integrability of generalized Zakharov-Shabat systems, focusing on CBC systems, their gauge equivalents, and associated Hamiltonian structures, advancing the theoretical understanding of these integrable models.

Contribution

It provides a detailed analysis of the properties of fundamental solutions, scattering data, and Hamiltonian hierarchies for CBC systems and their gauge equivalents, extending the inverse scattering framework.

Findings

Characterization of fundamental analytical solutions for gauge-equivalent systems

Description of minimal scattering data sets

Identification of integrable hierarchies and Hamiltonian structures

Abstract

The generalized Zakharov-Shabat systems with complex-valued Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studies. This includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations solvable by the inverse scattering method and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures.