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A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations

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Abstract

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Bäcklund transformation, and the method of solving a Riccati map by exploiting two known particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler’s lattice equation (or Q4).

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia

    James Atkinson

  2. School of Mathematics, The University of Leeds, Leeds, LS2 9JT, UK

    Frank Nijhoff

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  1. James Atkinson
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  2. Frank Nijhoff
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Correspondence to James Atkinson.

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Communicated by Y. Kawahigashi

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Atkinson, J., Nijhoff, F. A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations. Commun. Math. Phys. 299, 283–304 (2010). https://doi.org/10.1007/s00220-010-1076-x

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  • DOI: https://doi.org/10.1007/s00220-010-1076-x

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