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Fundam. Prikl. Mat., 2006, Volume 12, Issue 7, Pages 251–262 (Mi fpm1016)  

This article is cited in 4 scientific papers (total in 4 papers)

On the variational integrating matrix for hyperbolic systems

S. Ya. Startsev

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

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.

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English version:
Journal of Mathematical Sciences (New York), 2008, 151:4, 3245–3253

Bibliographic databases:

UDC: 517.956.3+517.972.7

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

Citation in format AMSBIB
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\paper On the variational integrating matrix for hyperbolic systems
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\vol 12
\issue 7
\pages 251--262
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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}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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.  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. V. Kiselev, J. W. van de Leur, “Symmetry algebras of Lagrangian Liouville-type systems”, Theoret. and Math. Phys., 162:2 (2010), 149–162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. 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.  mathnet  crossref
  • Фундаментальная и прикладная математика
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