The Cauchy problem for the Pavlov equation with large data

We prove a local solvability of the Cauchy problem for the Pavlov equation with large initial data by the inverse scattering method. The Pavlov equation arises in studies Einstein-Weyl geometries and dispersionless integrable models. Our theory yields a local solvability of Cauchy problems for a quasi-linear wave equation with a characteristic initial hypersurface.