# Manchester Geometry Seminar 2007/2008

**4 October 2007. ** *The Frank Adams Room (Room 1.212), the Alan Turing Building. 4pm*
## Integrability of Quasilinear Equations of the Second Order

Maxim Pavlov (P. N. Lebedev Physical Institute, Moscow)

` m.v.pavlov@lboro.ac.uk`

We consider integrable quasilinear equations by the method of hydrodynamic reductions. In such a case, these equations can be associated with so-called Vlasov-like (collisionless Boltzmann) equations and integrable hydrodynamic chains.

Consideration of one of these objects simultaneously leads to both others. That means that any integrable hydrodynamic chain contains an information about reconstruction of the corresponding Vlasov-like equation and a 2+1 quasilinear equation, and vice versa.

However, this procedure is not so obvious. In this talk we present an approach establishing these links and at the same time leading to an infinite set of particular solutions for all of these objects.