20 Sep 2010; Mat-Nat Faculty (UiTø), seminar room 208 B, Breivang. Monday 12:15-14:00.

Maxim Pavlov (Lebedev Physical Institute, Moscow, Russia)

"Benney hydrodynamic chain is an integrable system".

We suggest some special tools for description of integrability of the Benney hydrodynamic chain. We prove that the Benney chain is an integrable system. It means that the Benney chain possesses an infinite series of conservation laws, commuting flows and Hamiltonian structures.

We construct hydrodynamic reductions of this Benney chain, and discuss integrability of these reductions. Then we are able to construct particular solutions of these reductions, then solutions of the Benney hydrodynamic chain, then solutions of the three dimensional quasilinear systems of the second order associated with the Benney chain.