Elenco seminari del ciclo di seminari
“SISTEMI HAMILTONIANI INTEGRABILI”

We discuss how to select scattering data generating physically relevant (real nonsingular) solutions of the KP-2 in the $\bar\partial$ approach (generating spatially localized solutions) and in the finite-gap approach (generating pariodic solutions). In particular it will be shown, that in the both cases the direct and the inverse scattering transform for the Lax operator are regular without the small norm assumption.

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 associated with 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.