Symmetry analysis of cylindrical Helmholtz equation
Mehdi Nadjafikhah, Ali Mahdipour-Shirayeh
TL;DR
This paper analyzes the symmetry properties of the three-dimensional cylindrical Helmholtz equation, deriving invariants, solutions, and symmetry subgroups to facilitate understanding and solving the equation.
Contribution
It provides a comprehensive symmetry analysis, including invariants, general solutions, and classification of symmetry subgroups for the cylindrical Helmholtz equation.
Findings
Complete set of invariants derived
General solution expressed via invariants
Optimal symmetry subgroup system identified
Abstract
In this paper, we present the point symmetry group of three-dimensional homogeneous Helmholtz equation, when we consider the cylindrical coordinate system. In continuation, we present a complete set of functionally independent invariants of the equation along with the form of the general solution provided by these invariants. Finally, we find an optimal system of one-dimensional Lie subgroups of the full symmetry group.
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Taxonomy
TopicsDynamics and Control of Mechanical Systems · Vibration and Dynamic Analysis · Engineering Applied Research