Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 152, Pages 110–119 (Mi into355)  
Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations

S. Ya. Startsev

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
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Abstract: In this paper, we consider symmetry drivers (i.e., operators that map arbitrary functions of one of independent variables into symmetries) and formal integrals (i.e., operators that map symmetries to the kernel of the total derivative). We prove that a hyperbolic system of partial differential equations has a complete set of formal integrals if and only if it admits a complete set of symmetry drivers. This assertion is also valid for difference and differential-difference analogs of scalar hyperbolic equations.
Keywords: nonlinear hyperbolic systems, Darboux integrability, higher symmetries, conservation laws and integrals, Laplace invariants.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 252, Issue 2, Pages 232–241
DOI: https://doi.org/10.1007/s10958-020-05156-7
Bibliographic databases:
Document Type: Article
UDC: 517.957, 517.956.3, 514.763.8
MSC: 37K05, 37K10, 35L70, 39A14, 34K99
Language: Russian
Citation: S. Ya. Startsev, “Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations”, Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 152, VINITI, Moscow, 2018, 110–119; J. Math. Sci. (N. Y.), 252:2 (2021), 232–241
Citation in format AMSBIB
\Bibitem{Sta18}
\by S.~Ya.~Startsev
\paper Symmetry Drivers and Formal Integrals of Hyperbolic Systems of Equations
\inbook Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 152
\pages 110--119
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into355}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3903382}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 252
\issue 2
\pages 232--241
\crossref{https://doi.org/10.1007/s10958-020-05156-7}
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