Characterization of rational solutions of a KdV-like equation

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    Abstract

    We characterize the rational solutions to a KdV-like equation which are generated from polynomial solutions to the corresponding generalized bilinear equation. We use a particular class of polynomials satisfying a quadratic difference equation to obtain that there are no solutions of the bilinear equation with degree (in the spatial variable) greater than 5. As a byproduct, we answer positively a conjecture of Yi Zhang and Wen-Xiu Ma about these solutions.

    Original languageBritish English
    Pages (from-to)396-416
    Number of pages21
    JournalMathematics and Computers in Simulation
    Volume201
    DOIs
    StatePublished - Nov 2022

    Keywords

    • Generalized bilinear equation
    • KdV equation
    • Rational solution

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