Investigating symmetries and conservation laws of PDEs and systems

Subject Areas : Geometry

P. Kabi-nejad ¹

1 -

Received: 2025-03-01 Accepted : 2025-08-02 Published : 2025-08-08

Keywords: Approximate symmetry, generalized symmetry, Hamiltonian symmetry, $\mu$-symmetry, conservation law,

Abstract :

The main purpose of this article is to investigate some special kinds of symmetries and conservation laws of some partial differential equations (PDEs) and systems which play a significant role in physics. In fact, we review Lie point symmetry, approximate and generalized symmetry, Hamiltonian symmetry, $\mu$-symmetry and different approaches for evaluating conservation laws of PDEs and systems. Additionally, we discuss the effect of the change of variables on the bi-Hamiltonian structure of some equations and obtain the corresponding Hamiltonian formalism of the transformed equation.‎

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