Theoretical and Mathematical Physics

, Volume 155, Issue 2, pp 802–811 | Cite as

Symmetries of nonlinear hyperbolic systems of the Toda chain type

  • V. V. Sokolov
  • S. Ya. Startsev


We consider hyperbolic systems of equations that have full sets of integrals along both characteristics. The best known example of models of this type is given by two-dimensional open Toda chains. For systems that have integrals, we construct a differential operator that takes integrals into symmetries. For systems of the chosen type, this proves the existence of higher symmetries dependent on arbitrary functions.


Liouville equation Toda chain integral higher symmetry hyperbolic system of partial differential equations Noether theorem 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsChernogolovka, Moscow OblastRussia
  2. 2.Institute of Mathematics and Computing CenterRASUfaRussia

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