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October 9, 2025Open Communications in Nonlinear Mathematical Physics0 citationsOpen Access

Two sequences of fully-nonlinear evolution equations and their symmetry properties

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MEMarianna EulerNENorbert Euler

Key Points

  • The study reveals complete lie point symmetry algebras in two sequences of odd-order evolution equations, enhancing our understanding of their properties.
  • Key findings indicate both the third-order and fifth-order fully-nonlinear equations are identified as symmetry-integrable, contributing to the field of nonlinear dynamics.
  • A discussion on lie-bäcklund symmetries elaborates on the symmetry-integrability of the equations, providing a framework for future research.
  • The analysis spans nine pages, thoroughly covering the implications of the symmetry properties in mathematical physics.

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-Bäcklund symmetries and the consequent symmetry-integrability of the equations in the sequences are also discussed. 9 pages

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Cite This Study

Euler et al. (2025) studied this question.

synapsesocial.com/papers/68e70db290569dd607ee6434https://doi.org/10.46298/ocnmp.16486
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