Edoardo Peroni ; Jing Ping Wang - Hamiltonian and recursion operators for a discrete analogue of the Kaup-Kupershmidt equation

ocnmp:11545 - Open Communications in Nonlinear Mathematical Physics, February 15, 2024, Special Issue in Memory of Decio Levi - https://doi.org/10.46298/ocnmp.11545
Hamiltonian and recursion operators for a discrete analogue of the Kaup-Kupershmidt equationArticle

Authors: Edoardo Peroni ; Jing Ping Wang

    In this paper we study the algebraic properties of a new integrable differential-difference equation. This equation can be seen as a deformation of the modified Narita-Itoh-Bogoyavlensky equation and has the Kaup-Kupershmidt equation in its continuous limit. Using its Lax representation we explicitly construct a recursion operator for this equation and prove that it is a Nijenhuis operator. Moreover, we present the bi-Hamiltonian structures for this new equation.

    https://doi.org/10.46298/ocnmp.11545
    Source: arXiv.org:2306.14869
    Volume: Special Issue in Memory of Decio Levi
    Published on: February 15, 2024
    Accepted on: November 29, 2023
    Submitted on: July 5, 2023
    Keywords: Nonlinear Sciences - Exactly Solvable and Integrable Systems
    Licence: arXiv.org - Non-exclusive license to distribute

    Classifications

    Mathematics Subject Classification 20201
    Sources:
    • [1] zbMATH Open.

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