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

James Atkinson, Frank Nijhoff

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    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).
    Original languageEnglish
    Pages (from-to)283-304
    JournalCommunications in Mathematical Physics
    Volume299
    Issue number2
    DOIs
    Publication statusPublished - 2010

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