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TMF, 1998, Volume 116, Number 2, Pages 193–200 (Mi tmf897)  

This article is cited in 3 scientific papers (total in 3 papers)

Equations invariant under differential substitutions

V. S. Novikov

L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: The classification of differential autosubstitutions of the form $\hat u=G(u_x,u)$ that are allowed by general evolution equations with one spatial variable is considered. In the one-field case, every such substitution can be reduced to the autosubstitution $\hat u=u+u_x/u$ for the Burgers equation by a point transformation. This substitution is generalized to the two-field case.

DOI: https://doi.org/10.4213/tmf897

Full text: PDF file (179 kB)

English version:
Theoretical and Mathematical Physics, 1998, 116:2, 890–895

Bibliographic databases:

Received: 05.03.1998

Citation: V. S. Novikov, “Equations invariant under differential substitutions”, TMF, 116:2 (1998), 193–200; Theoret. and Math. Phys., 116:2 (1998), 890–895

Citation in format AMSBIB
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\paper Equations invariant under differential substitutions
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\issue 2
\pages 193--200
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\zmath{https://zbmath.org/?q=an:0916.35105}
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\transl
\jour Theoret. and Math. Phys.
\yr 1998
\vol 116
\issue 2
\pages 890--895
\crossref{https://doi.org/10.1007/BF02557131}
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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. S. Ya. Startsev, “Hyperbolic Equations Admitting Differential Substitutions”, Theoret. and Math. Phys., 127:1 (2001), 460–470  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Tryhuk, V, “AUTOMORPHISMS OF CURVES”, Journal of Nonlinear Mathematical Physics, 16:3 (2009), 259  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Uenal G., Turkeri H., Khalique Ch.M., “Explicit Solution Processes for Nonlinear Jump-Diffusion Equations”, J Nonlinear Math Phys, 17:3 (2010), 281–310  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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