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# Darboux integrability of discrete 2D Toda lattices

GFM seminar
FCUL, C6, room 6.2.33
2019-06-19 11:00 .. 12:00
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by Sergey V. Smirnov (Moscow State University)

Equations that are known now as the "two-dimensional Toda lattice" have in fact appeared in classical differential geometry in the end of 19th century. Generalized 2D-Toda lattices corresponding to the Cartan matrices of simple Lie algebras are Darboux integrable, that is, they admit complete families of essentially independent integrals along both characteristics. We consider semi-discrete and purely discrete analogs of these systems and prove their Darboux integrability which appears to be a direct consequence of the nature of Toda lattice related to Darboux-Laplace transformations.

If there is enough time, we will also discuss the notion of characteristic algebra which is an algebraic structure that controls the existence of characteristic integrals for a hyperbolic equation and its growth properties describe the behaviour of the corresponding hyperbolic system.