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Teoreticheskaya i Matematicheskaya Fizika, 1988, Volume 75, Number 1, Pages 18–25 (Mi tmf4663)  
This article is cited in 6 scientific papers (total in 6 papers)

On straightening the characteristics of a quasilinear second-order equation

F. Kh. Mukminov
Full-text PDF (810 kB) Citations (6)
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Abstract: An invertible transformation that preserves the class of quasilinear second-order equations is proposed. Necessary and sufficient conditions are found under which this transformation carries a quasilinear equation into an equation with straight characteristics. For one quasilinear equation the general solution is found by means of the transformation. Examples of Lagrangians of the form L(u,uxuy) possessing conservation laws of high order are given.
Received: 26.11.1986
English version:
Theoretical and Mathematical Physics, 1988, Volume 75, Issue 1, Pages 340–345
DOI: https://doi.org/10.1007/BF01017167
Bibliographic databases:
Language: Russian
Citation: F. Kh. Mukminov, “On straightening the characteristics of a quasilinear second-order equation”, TMF, 75:1 (1988), 18–25; Theoret. and Math. Phys., 75:1 (1988), 340–345
Citation in format AMSBIB
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\by F.~Kh.~Mukminov
\paper On straightening the characteristics of a~quasilinear second-order equation
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\vol 75
\issue 1
\pages 18--25
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=955664}
\zmath{https://zbmath.org/?q=an:0684.35005}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 75
\issue 1
\pages 340--345
\crossref{https://doi.org/10.1007/BF01017167}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988U172800002}
Linking options:
  • https://www.mathnet.ru/eng/tmf4663
  • https://www.mathnet.ru/eng/tmf/v75/i1/p18
    • This publication is cited in the following 6 articles:
    1. S. Ya. Startsev, “On Bäcklund Transformations Preserving the Darboux Integrability of Hyperbolic Equations”, Lobachevskii J Math, 44:5 (2023), 1929  crossref
    2. Ferapontov E.V. Moss J., “Linearly Degenerate Partial Differential Equations and Quadratic Line Complexes”, Commun. Anal. Geom., 23:1 (2015), 91–127  isi
    3. S. I. Svinolupov, V. V. Sokolov, “Factorization of evolution equations”, Russian Math. Surveys, 47:3 (1992), 127–162  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. L Bombelli, W E Couch, R J Torrence, “Solvable systems of wave equations and non-Abelian Toda lattices”, J. Phys. A: Math. Gen., 25:5 (1992), 1309  crossref
    5. E. V. Ferapontov, “Integration of weekly nonlinear semi-hamiltonian systems of hydrodynamic type by methods of the theory of webs”, Math. USSR-Sb., 71:1 (1992), 65–79  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. V. A. Andreev, “Matrix sine-Gordon equation”, Theoret. and Math. Phys., 84:3 (1990), 920–929  mathnet  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:85
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