Elenco seminari del ciclo di seminari
“NONLOCALITY AND SCATTERING TRANSFORM FOR FOR MULTIDIMENSIONAL DISPERSIONLESS SYSTEMS”

At the present time the class of dispersionless integrable systems attracts serious attention. Manakov and Santini suggested a modification of the scattering transform for vector fields, which is appropriate for integration of multidimensional dispersionless systems, but it requires seriuos additional work to make it sufficiently strict. We provide first strict results in this area.

Multidimensional integrable systems are usually non-local, therefore the solutions of the Cauchy problem depend on a proper choice of intergration constants. The inverse scattering transform usually prescribe a special choice of these constants. We calculate this choice for the model example of the Pavlov equation. The final answer can be explained using a lemma form integral geometry.