Elliptic N-soliton Solutions of ABS Lattice Equations

Frank Nijhoff, James Atkinson

    Research output: Contribution to journalArticlepeer-review

    26 Citations (Scopus)


    Elliptic N-soliton-type solutions, that is, solutions emerging from the application of N consecutive Bäcklund transformations to an elliptic seed solution, are constructed for all equations in the Adler-Bobenko-Suris (ABS) list of quadrilateral lattice equations, except for the case of the Q4 equation which is treated elsewhere. The main construction, which is based on an elliptic Cauchy matrix, is performed for the equation Q3, and by coalescence on certain auxiliary parameters, the corresponding solutions of the remaining equations in the list are obtained. Furthermore, the underlying linear structure of the equations is exhibited, leading, in particular, to a novel Lax representation of the Q3 equation.
    Original languageEnglish
    Pages (from-to)3837-3895
    JournalInternational Mathematics Research Notices
    Issue number20
    Publication statusPublished - 2010


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