Two sequences of fully-nonlinear evolution equations and their symmetry properties
Exactly Solvable and Integrable Systems
2025-10-23 v4
Abstract
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-B\"acklund symmetries and the consequent symmetry-integrability of the equations in the sequences are also discussed.
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Cite
@article{arxiv.2509.05535,
title = {Two sequences of fully-nonlinear evolution equations and their symmetry properties},
author = {Marianna Euler and Norbert Euler},
journal= {arXiv preprint arXiv:2509.05535},
year = {2025}
}
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9 pages