Marianna Euler ; Norbert Euler - Two sequences of fully-nonlinear evolution equations and their symmetry properties

ocnmp:16486 - Open Communications in Nonlinear Mathematical Physics, October 7, 2025, Volume 5 - https://doi.org/10.46298/ocnmp.16486
Two sequences of fully-nonlinear evolution equations and their symmetry propertiesArticle

Authors: Marianna Euler ; Norbert Euler

    We obtain the complete Lie point symmetry algebras of two sequences of odd-order evolution equations. This includes equations that are fully-nonlinear, i.e. nonlinear in the highest derivative. Two of the equations in the sequences have recently been identified as symmetry-integrable, namely a 3rd-order equation and a 5th-order equation [Open Communications in Nonlinear Mathematical Physics, Special Issue in honour of George W Bluman, ocnmp:15938, 1--15, 2025]. These two examples provided the motivation for the current study. The Lie-Bäcklund symmetries and the consequent symmetry-integrability of the equations in the sequences are also discussed.

    9 pages


    Volume: Volume 5
    Published on: October 7, 2025
    Accepted on: October 6, 2025
    Submitted on: September 9, 2025
    Keywords: Exactly Solvable and Integrable Systems