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On some new forms of lattice integrable equations

  • Research Article
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Central European Journal of Physics

Abstract

Inspired by the forms of delay-Painleve equations, we consider some new differential-discrete systems of KdV, mKdV and Sine-Gordon — type related by simple one way Miura transformations to classical ones. Using Hirota bilinear formalism we construct their new integrable discretizations, some of them having higher order. In particular, by this procedure, we show that the integrable discretization of intermediate sine-Gordon equation is exactly lattice mKdV and also we find a bilinear form of the recently proposed lattice Tzitzeica equation. Also the travelling wave reduction of these new lattice equations is studied and it is shown that all of them, including the higher order ones, can be integrated to Quispel-Roberts-Thomson (QRT) mappings.

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Authors and Affiliations

  1. Dept. of Physics, University of Craiova, 13 A.I. Cuza, 200585, Craiova, Romania

    Corina N. Babalic

  2. Dept. of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Atomistilor 407, 077125, Magurele, Bucharest, Romania

    Corina N. Babalic & Adrian S. Carstea

Authors
  1. Corina N. Babalic
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  2. Adrian S. Carstea
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Correspondence to Corina N. Babalic.

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Babalic, C.N., Carstea, A.S. On some new forms of lattice integrable equations. centr.eur.j.phys. 12, 341–347 (2014). https://doi.org/10.2478/s11534-014-0455-x

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  • DOI: https://doi.org/10.2478/s11534-014-0455-x

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