Journal of Mathematical Sciences

, Volume 151, Issue 4, pp 3245–3253 | Cite as

On the variational integrating matrix for hyperbolic systems

  • S. Ya. StartsevEmail author


We obtain a necessary and sufficient condition for a hyperbolic system to be an Euler-Lagrange system with a first-order Lagrangian up to multiplication by some matrix. If this condition is satisfied and an integral of the system is known to us, then we can construct a family of higher symmetries that depend on an arbitrary function. Also, we consider the systems that satisfy the above criterion and that possess a sequence of the generalized Laplace invariants with respect to one of the characteristics; then we prove that the generalized Laplace invariants with respect to the other characteristic are uniquely defined.


Vector Function Hyperbolic System Total Derivative Variational Derivative Lagrange System 
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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute for Mathematics UNCRASMoscowRussia

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