In this paper, the logarithmic Monge–Ampère flow evolution equation is studied by the classical Lie symmetry analysis method. First, the optimal system was obtained by the adjoint representation table. Second, by performing symmetric transformation on the optimal system, the corresponding ordinary differential equations are obtained, and the Jacobian elliptic function solution, the periodic solution and the power series solution are constructed. Finally, the dynamical behaviors of the solutions are described by choosing arbitrary parameters.

中文翻译：

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对数Monge-Ampère流演化方程的李对称分析、精确解和幂级数解

本文采用经典李对称分析方法研究对数Monge-Ampère流动演化方程。首先，通过伴随表示表得到最优系统。其次，通过对最优系统进行对称变换，得到相应的常微分方程，构造雅可比椭圆函数解、周期解和幂级数解。最后，通过选择任意参数来描述解的动态行为。