Abstract:
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.
Citation:
S. Ya. Startsev, “On the variational integrating matrix for hyperbolic systems”, Fundam. Prikl. Mat., 12:7 (2006), 251–262; J. Math. Sci., 151:4 (2008), 3245–3253
\Bibitem{Sta06}
\by S.~Ya.~Startsev
\paper On the variational integrating matrix for hyperbolic systems
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 7
\pages 251--262
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\zmath{https://zbmath.org/?q=an:1158.35311}
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\transl
\jour J. Math. Sci.
\yr 2008
\vol 151
\issue 4
\pages 3245--3253
\crossref{https://doi.org/10.1007/s10958-008-9034-2}
\elib{https://elibrary.ru/item.asp?id=13587592}
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Linking options:
https://www.mathnet.ru/eng/fpm1016
https://www.mathnet.ru/eng/fpm/v12/i7/p251
This publication is cited in the following 6 articles:
I. V. Rakhmelevich, “Ob invariantakh Laplasa dvumernykh nelineinykh uravnenii vtorogo poryadka s odnorodnym polinomom”, Izv. vuzov. Matem., 2024, no. 8, 55–64
I. V. Rakhmelevich, “On Laplace Invariants of Two-Dimensional Nonlinear Equations of the Second Order with Homogeneous Polynomial”, Russ Math., 68:8 (2024), 47
Sergey Ya. Startsev, “Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries”, SIGMA, 13 (2017), 034, 20 pp.
A. V. Kiselev, J. W. van de Leur, “Symmetry algebras of Lagrangian Liouville-type systems”, Theoret. and Math. Phys., 162:2 (2010), 149–162
Demskoi D.K., Lee Jyh-Hao, “On non-abelian Toda A(1)2 model and related hierarchies”, J. Math. Phys., 50:12 (2009), 123516, 11 pp.
V. V. Sokolov, S. Ya. Startsev, “Symmetries of nonlinear hyperbolic systems of the Toda chain type”, Theoret. and Math. Phys., 155:2 (2008), 802–811
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