Non-diagonalisable integrable systems of hydrodynamic type: geometry, solutions and Hamiltonian formalism

Karoline van Gemst (Universita degli Studi di Milano-Bicocca)

Tuesday 11th November 16:00-17:00
Maths 311B

Abstract

Integrable systems of hydrodynamic type consist of partial differential equations of the form  u^i_t = V^i_j(u) u^j_x , where i = 1, ..., n, and arise naturally in many areas of mathematics and physics. The theory often assumes that the matrix V is diagonalisable.  Such systems have been extensively studied, and their structure is well understood. Many interesting systems, however, are related to non-diagonalisable systems, and in this case the theory is much less developed.  

In three recent papers, Paolo Lorenzoni, Sara Perletti, and I developed the theory for a class of non-diagonalisable systems  under the assumption that the matrix V is block-diagonalisable. In this talk, after introducing the necessary definitions, I will present the main results of these papers; how the correspondence with F-manifolds, solution methods, and the construction of Hamiltonian densities and metrics, extend to the regular setting.

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