Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the scattering and inverse scattering problem, recently introduced just at a formal level, for integrable dispersionless PDEs, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data.