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 for integrable dispersionless
PDEs, recently introduced just at a formal level, 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.Comment: In the new version the analytical technique was essentially revised.
The previous version contained a wrong statement about the solvability of the
inverse problem for large data. This problem remains ope
