一类自伴随Lubrication方程的对称,守恒律,拉格朗日函数和精确解

On the Class of Self-Adjoint Lubrication Equation:Symmetries,Conservation Laws,Lagrangians and Exact Solutions

本文借助李对称分析研究了一类自伴随的Lubrication方程,此类方程可用来描述液体薄膜动力学行为.基于非奇异的局域守恒律乘子和李对称方法,我们系统地推导出了此类方程的局域守恒律,非局域相关系统,李对称和一些有趣的精确解.此模型的非局域相关系统在本文中被首次研究,可用于寻找原方程更丰富的解空间.此外,基于局域守恒律和变分原则,我们推导出原方程的四类拉格朗日函数.

In this work,the class of self-adjoint lubrication(SAL) equation is investigated,which is an important model of various nonlinear real situations describing the dynamics of thin liquid films.By applying a set of non-singular local multipliers and the classical Lie method,we systematically present the complete set of local conservation laws,nonlocally related PDE systems,Lie symmetries and some interesting analytical solutions of the equation for an arbitrary constant a.Here it is the first time to investigate the nonlocally related PDE systems for this model,which can be used to expand the solution space of the given PDE system.Furthermore,by using its local conservation laws and variational principle,we obtain four kinds of Lagrangians.