Fine Structure of Matrix Darboux-Toda Integrable Mapping

TL;DR

This paper introduces a novel class of discrete transformations for the matrix nonlinear Schrödinger system, revealing that the matrix Darboux-Toda transformation can be decomposed into symmetry-preserving mappings.

Contribution

It demonstrates that the matrix Darboux-Toda transformation can be expressed as a product of mappings, each being a symmetry of the matrix nonlinear Schrödinger system, thus introducing new discrete transformations.

Findings

Decomposition of Darboux-Toda transformation into symmetry mappings

Introduction of new discrete transformations for the matrix nonlinear Schrödinger system

Realization of these mappings in the context of vector nonlinear Schrödinger system

Abstract

We show here that matrix Darboux-Toda transformation can be written as a product of a number of mappings. Each of these mappings is a symmetry of the matrix nonlinear Shrodinger system of integro-differential equations. We thus introduce a completely new type of discrete transformations for this system. The discrete symmetry of the vector nonlinear Shrodinger system is a particular realization of these mappings.