This article is cited in 11 papers

One Class of Liouville-Type Systems

D. K. Demskoi

Orel State University

Abstract: We prove that a class of systems with the Lagrangian of the form $L=\bigl[g_{ij}(u)u^i_xu^j_t\bigr]/2+f(u)$ is of the Liouville type. We construct new integrable Hamiltonian systems related to the symmetries of the hyperbolic systems under consideration by substitutions of the Miura transformation type. For one of the systems obtained, we construct the second-order recursion operator.

Keywords: system of Liouville type, higher pseudoconstants, recursion operator.

Received: 13.10.2003
Revised: 16.03.2004

DOI: 10.4213/tmf121

 English version: Theoretical and Mathematical Physics, 2004, 141:2, 1509–1527

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