Liénard型方程$\ddot{x}+f(x)\dot{x}+g(x) = 0$中可积方程的群论识别：第II部分：具有极大Lie点对称性的方程
A Group Theoretical Identification of Integrable Equations in the Liénard Type Equation $\ddot{x}+f(x)\dot{x}+g(x) = 0$ : Part II: Equations having Maximal Lie Point Symmetries
摘要：
在这第二组的两个文件的李对称性分析的一类Liénard型方程的形式$\ddot {x} + f(x)\dot {x} + g(x)= 0$，其中过点表示微分关于时间和$f(x)$和$g(x)$是光滑函数的变量，我们隔离的方程具有最大的李点对称性。众所周知，任何二阶非线性常微分方程，只要具有八参数李点对称性，都可以通过点变换线性化为自由粒子方程。因此，所有确定的方程都是可线性化的。我们还证明了只有当$f_{xx} =0$（下标表示微分）时，才能得到上述Liénard方程的极大Lie点对称.此外，我们还讨论了本文中所确定的所有非线性方程的线性化变换和解。
英文摘要：
In this second of the set of two papers on Lie symmetry analysis of a class of Liénard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are smooth functions of their variables, we isolate the equations which possess maximal Lie point symmetries. It is well known that any second order nonlinear ordinary differential equation which admits eight parameter Lie point symmetries is linearizable to free particle equation through point transformation. As a consequence all the identified equations turn out to be linearizable. We also show that one can get maximal Lie point symmetries for the above Liénard equation only when $f_{xx} =0$ (subscript denotes differentiation). In addition, we discuss the linearising transformations and solutions for all the nonlinear equations identified in this paper.
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