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TMF, 1997, Volume 110, Number 2, Pages 233–241 (Mi tmf964)  

This article is cited in 7 scientific papers (total in 7 papers)

Some generalizations of the 2-dimensional Toda chain and $\operatorname{sh}$-Gordon equation

A. I. Zenchuk

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

Abstract: We study the discrete transformations of the solutions and potentials of the second order partial differential equation with two independent variables. These transformations are introduced by the formula $D=V_1\partial_x+V_2\partial_y+V_3$. The simplest closed chains of these transformations are considered. The integrability of the derived nonlinear equations by the IST-method is proved.

DOI: https://doi.org/10.4213/tmf964

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English version:
Theoretical and Mathematical Physics, 1997, 110:2, 183–189

Bibliographic databases:

Received: 19.06.1996

Citation: A. I. Zenchuk, “Some generalizations of the 2-dimensional Toda chain and $\operatorname{sh}$-Gordon equation”, TMF, 110:2 (1997), 233–241; Theoret. and Math. Phys., 110:2 (1997), 183–189

Citation in format AMSBIB
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\paper Some generalizations of the 2-dimensional Toda chain and $\operatorname{sh}$-Gordon equation
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\vol 110
\issue 2
\pages 233--241
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\jour Theoret. and Math. Phys.
\yr 1997
\vol 110
\issue 2
\pages 183--189
\crossref{https://doi.org/10.1007/BF02630444}
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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. A. V. Yurov, “Conjugate chains of discrete symmetries in $(1+2)$ nonlinear equations”, Theoret. and Math. Phys., 119:3 (1999), 731–738  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Kraenkel, RA, “Two-dimensional integrable generalization of the Camassa-Holm equation”, Physics Letters A, 260:3–4 (1999), 218  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Kraenkel, RA, “Camassa-Holm equation: transformation to deformed sinh-Gordon equations, cuspon and soliton solutions”, Journal of Physics A-Mathematical and General, 32:25 (1999), 4733  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. Zenchuk, AI, “Multidimensional hierarchies of (1+1)-dimensional integrable partial differential equations. Nonsymmetric partial derivative-dressing”, Journal of Mathematical Physics, 41:9 (2000), 6248  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Kraenkel, RA, “Modified Korteweg-de Vries hierarchy with hodograph transformation: Camassa-Holm and Harry-Dym hierarchies”, Mathematics and Computers in Simulation, 55:4–6 (2001), 483  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Zenchuk A.I., “The spectral problem and particular solutions to the (2+1)-dimensional integrable generalization of the Camassa-Holm equation”, Physica D, 152 (2001), 178–188  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Leble, SB, “Reduction restrictions of Darboux and Laplace transformations for the Goursat equation”, Journal of Mathematical Physics, 43:2 (2002), 1095  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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