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

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.