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Classification of discrete systems on a square lattice

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Abstract

We consider the classification up to a Möbius transformation of real linearizable and integrable partial difference equations with dispersion defined on a square lattice by the multiscale reduction around their harmonic solution. We show that the A1, A2, and A3 linearizability and integrability conditions constrain the number of parameters in the equation, but these conditions are insufficient for a complete characterization of the subclass of multilinear equations on a square lattice.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, Escuela Universitaria de Ingeniería Técnica de Telecomunicación, Madrid, Spain

    R. Hernández Heredero

  2. Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre and Sezione INFN, Roma Tre, Rome, Italy

    D. Levi & C. Scimiterna

Authors
  1. R. Hernández Heredero
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  2. D. Levi
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  3. C. Scimiterna
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Correspondence to R. Hernández Heredero.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 172, No. 2, pp. 250–263, August, 2012.

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Hernández Heredero, R., Levi, D. & Scimiterna, C. Classification of discrete systems on a square lattice. Theor Math Phys 172, 1097–1108 (2012). https://doi.org/10.1007/s11232-012-0098-2

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