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Some generalizations of the two-dimensional Toda chain and Sinh-Gordon equations

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Abstract

We investigate discrete transformations of the solutions and potentials of a scalar differential equation of the second order with two independent variables. The transformations are implemented by the operator D=V1ϱx+V2ϱy+V3 and simple cases of the closure of these transformations are considered. Inverse scattering problem methods are used to prove the integrability of the nonlinear equations obtained.

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Authors and Affiliations

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

    A. I. Zenchuk

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  1. A. I. Zenchuk
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 233–241, February, 1997.

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Zenchuk, A.I. Some generalizations of the two-dimensional Toda chain and Sinh-Gordon equations. Theor Math Phys 110, 183–189 (1997). https://doi.org/10.1007/BF02630444

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  • DOI: https://doi.org/10.1007/BF02630444

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