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Integrable Two-Dimensional Lattices. Characteristic Lie Rings and Classification

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Abstract

This paper is devoted to the problem of classification of integrable nonlinear models with three independent variables. The classification algorithm based on the notion of characteristic Lie rings is applied to a class of two-dimensional lattices of hydrodynamic type. By imposing appropriate cutting-off boundary conditions, we reduce the lattice to a system of hyperbolic equations, which is assumed to be a Darboux integrable system. As a result, we found a new integrable lattice.

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Authors and Affiliations

  1. Institute of Mathematics, Ufa Scientific Center of the Russian Academy of Sciences, Ufa, Russia

    I. T. Habibullin & M. N. Poptsova

  2. Bashkir State University, Ufa, Russia

    I. T. Habibullin

Authors
  1. I. T. Habibullin
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  2. M. N. Poptsova
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Correspondence to I. T. Habibullin.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 140, Differential Equations. Mathematical Physics, 2017.

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Habibullin, I.T., Poptsova, M.N. Integrable Two-Dimensional Lattices. Characteristic Lie Rings and Classification. J Math Sci 241, 396–408 (2019). https://doi.org/10.1007/s10958-019-04432-5

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  • DOI: https://doi.org/10.1007/s10958-019-04432-5

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