Theoretical and Mathematical Physics

, Volume 141, Issue 2, pp 1509–1527 | Cite as

One Class of Liouville-Type Systems

  • D. K. Demskoi


We prove that a class of systems with the Lagrangian of the form \(L = {{\left[ {g_{\{ ij\} } (u)u_x^i u_t^j } \right]} \mathord{\left/ {\vphantom {{\left[ {g_{\{ ij\} } (u)u_x^i u_t^j } \right]} {2 + f(u)}}} \right. \kern-\nulldelimiterspace} {2 + f(u)}}\) 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.

system of Liouville type higher pseudoconstants recursion operator 


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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • D. K. Demskoi
    • 1
  1. 1.Orel State UniversityOrelRussia

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