In this paper, based on the classical symmetry method, the group-invariant solutions of the evolution equation of a hyperbolic curve flow are investigated. The optimal system of the obtained symmetries is found, and the reduced equations and exact solutions of the evolution equation are discussed. Then explicit solutions are obtained by the power series method. In addition, the convergence of the power series solutions is proved. The objective shapes of the solutions of the evolution equation are performed.

中文翻译：

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基于李对称法的双曲线流演化方程分析

本文基于经典的对称性方法，研究了双曲线流演化方程的群不变解。找到了所获得对称性的最优系统，并讨论了演化方程的简化方程和精确解。然后通过幂级数方法得到显式解。此外，证明了幂级数解的收敛性。执行演化方程解的客观形状。