Approximate symmetries of the Harry Dym equation
Mehdi Nadjafikhah, Parastoo Kabi-Nejad
TL;DR
This paper derives approximate symmetries for the Harry Dym equation using a specific method, analyzes its Lie algebra structure, and identifies invariants and optimal subalgebras.
Contribution
It introduces the first order approximate symmetries for the Harry Dym equation and explores its Lie algebra structure and invariants.
Findings
Derived first order approximate symmetries for the Harry Dym equation
Analyzed the Lie algebra structure of the perturbed equation
Computed the optimal system of subalgebras and invariants
Abstract
In this paper, we derive the first order approximate symmetries for the Harry Dym equation by the method of approximate transformation groups proposed by Baikov, Gaszizov and Ibragimov. Moreover, we investigate the structure of the Lie algebra of symmetries of the perturbed Harry Dym equation. We compute the one-dimensional optimal system of subalgebras as well as point out some approximately differential invariants with respect to the generators of Lie algebra and optimal system.
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