圆柱Helmholtz方程的对称性分析
Symmetry analysis of cylindrical Helmholtz equation
摘要：
本文给出了三维齐次Helmholtz方程在柱坐标系下的点对称群。在延续中，我们提出了一套完整的功能独立的不变量的方程，以及由这些不变量提供的一般解决方案的形式。最后，我们找到了全对称群的一维李群的最优系统。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
