This article is cited in 19 papers

Laplace Invariants of Two-Dimensional Open Toda Lattices

A. M. Gurieva^a, A. V. Zhiber<sup>b

a</sup> Ufa State Aviation Technical University
^b Institute of Mechanics, Ufa Centre of the Russian Academy of Sciences

Abstract: We show that Toda lattices with the Cartan matrices $\mathrm{A}_{n}$, $\mathrm{B}_{n}$, $\mathrm{C}_{n}$ и $\mathrm{D}_{n}$ are Liouville-type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants. We show how they can be used to construct conservation laws ($x$ and $y$ integrals) and higher symmetries.

Keywords: symmetries, integrals, Laplace invariants, generalized invariants.

Received: 24.03.2003

DOI: 10.4213/tmf28

 English version: Theoretical and Mathematical Physics, 2004, 138:3, 338–355

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