Discrete and Backlund (!) transformations of SDYM system

TL;DR

This paper explores discrete and Backlund transformations of the self-dual Yang-Mills (SDYM) system, revealing how these transformations generate new solutions using arbitrary functions, thus enriching the solution space.

Contribution

It introduces a Backlund transformation for SDYM equations involving arbitrary functions, expanding the methods for generating solutions within gauge theories.

Findings

Transformation depends on 2N_G arbitrary functions of two variables

Transforms preserve the physically restricted solution class

Provides a new approach to solution generation in SDYM systems

Abstract

Symmetry of SDYM equations for "physically restricted solution" with hermitian group element $G=G^H$ in representation of Yang is described. Such transformation $D^B$ pass some PRS to the new one of the same kind. Transformation contain $2N_G$ arbirtrary functions of two independent arguments, where $N_G$ dimension of the gauge semi-simple algebra. These functions may be considered as additional parameters typical for Backlund aproach and by this reason we use term Backlund for this transformation.