What type of study is this?

This is a Quantitative Study study.

October 9, 2025Open Access

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

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

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

Key Points

Abstract

Cite This Study