一种非线性系统的群叶状方法

A group foliation method for nonlinear systems

通过研究等价活动标架理论与非线性系统精确解的关系,提出一种基于活动标架理论的群叶状方法来求解微分方程的精确解,并用计算机代数得到了1+1维非线性偏微分方程的变量分离的新精确解,验证了群叶状方法的有效性和便捷性。从而推广和丰富了非线性系统的研究内容,该方法也适用于其他的复杂非线性系统。

A group foliation method of moving frames theory is proposed to solve the exact solution of differential equation by researching the relationship between the equivalent moving frames and the exact solution of nonlinear systems.Computer algebra is employed to get the variable separation solutions of group foliation of the 1+1 dimensional nonlinear partial differential equation,proving the effectiveness and accessibility of the group foliation method.Therefore,the research on nonlinear systems is extended and enriched.The proposed method is also applicable to other complex nonlinear systems.