一类四阶偏微分方程的对称分析及级数解

摘要

In the paper, Lie symmetry analysis of a fourth-order partial differential equation is performed. The one dimension optimal system of the Lie symmetries admitted by the equation in consideration is constructed. In addition, all exact solutions or the reduced equations corresponding to the optimal system are presented. Furthermore, based on the power series theory, a kind of explicit power series solutions for the equation is well constructed with a detailed derivation.%研究了一类四阶偏微分方程的李对称，构造了方程所容许的李对称的优化系统，进行了对称约化，得到了精确解。进一步，基于幂级数理论，得到了这类四阶偏微分方程的幂级数解。