Special singular solutions of soliton equations and indefinite scalar products.

by P.G. Grinevich (Landau Institute for Theoretical Physics Russian Academy of Sciences)

Monday 16 Jan 2017, 14:00 → 15:30 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

In the soliton theory, generic singular Cauchy data usually do not generate good solutions. But if the singularities are chosen in a special way, their form is compatible with the time dynamics. The first example of such type is given by rational Korteweg-de Vries solutions; the scattering transform for such potentials was developed by Arkadiev, Pogrebkov and Polivanov. We show that the scattering transform for these potentials can be naturally interpreted in terms of pseudo-Hilbert spaces, and the number of negative squares gives a new integral of motion.