Abstract:
A criterion for the interruption of the sequence of generalized Laplace invariants is found. A general solution of a system of linear hyperbolic equations with zero invariants is constructed.
Citation:
A. V. Zhiber, Yu. G. Mikhailova, “On hyperbolic systems of equations with zero generalized Laplace invariants”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 4, 2007, 74–83; Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S154–S164
\Bibitem{ZhiMik07}
\by A.~V.~Zhiber, Yu.~G.~Mikhailova
\paper On hyperbolic systems of equations with zero generalized Laplace invariants
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2007
\vol 13
\issue 4
\pages 74--83
\mathnet{http://mi.mathnet.ru/timm119}
\elib{https://elibrary.ru/item.asp?id=12040799}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2008
\vol 261
\issue , suppl. 1
\pages S154--S164
\crossref{https://doi.org/10.1134/S0081543808050143}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-66149185311}
Linking options:
https://www.mathnet.ru/eng/timm119
https://www.mathnet.ru/eng/timm/v13/i4/p74
This publication is cited in the following 4 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
Yu. G. Voronova, A. V. Zhiber, “Symmetries and Goursat problem for system of equations uxy=eu+vuy, vxy=−eu+vvy”, Ufa Math. J., 5:3 (2013), 20–27
A. V. Zhiber, Yu. G. Mikhailova, “Algoritm postroeniya obschego resheniya n-komponentnoi giperbolicheskoi sistemy uravnenii s nulevymi invariantami Laplasa i kraevye zadachi”, Ufimsk. matem. zhurn., 1:3 (2009), 28–45
Citation in format AMSBIB
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