A dispersionless integrable system associated to Diff(S1) gauge theory

A dispersionless integrable system underlying (2+1)-dimensional hyperCR Einstein-Weyl structures is obtained as a symmetry reduction of the anti-self-dual Yang-Mills equations with the gauge group Diff(S1). Two special classes of solutions are obtained from well known soliton equations by embedding SU(1,1) in Diff(S1).