FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 7, PAGES 251-262

On the variational integrating matrix for hyperbolic systems

S. Ya. Startsev

Abstract

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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.

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Last modified: February 13, 2007