Differential and other reductions of the self-dual conformal structure equations

TL;DR

This paper explores reductions of the self-dual conformal structure equations, including differential reductions, to construct solutions and analyze their relations within integrable systems in signature (2,2).

Contribution

It introduces characteristic reductions of the SDCS equations using Lax pairs, hierarchy, and dressing schemes, and presents the type B SDCS system.

Findings

Constructed solutions for SDCS equations using reductions

Analyzed relations between type B and original SDCS systems

Identified rich structure of reductions in the integrability framework

Abstract

The dispersionless integrable system we consider here was introduced to the literature rather recently, it is connected with the general local form of self-dual conformal structure (SDCS) for the signature (2,2). In integrability framework this system possesses a rich structure of reductions, including differential reductions. We will discuss several characteristic reductions for this system, using the Lax pair, hierarchy structure and the dressing scheme. We use reductions to construct solutions for the SDCS equations. One of our goals is to present type B SDCS system and consider its relations with the SDCS system.