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摘要: 将扩展Prelle-Singer法（扩展P-S法）用于求x=1（x，y），y=2（x，y）类型的二阶非线性耦合动力学系统的守恒量，得到了积分乘子满足的微分方程与守恒量的一般形式，并讨论所得守恒量的Noether对称性与Lie对称性.最后用扩展P-S法求得了四次非谐振子系统的两个守恒量，并讨论了系统的对称性.
Abstract: The extended Prelle-Singer method is used to find the conserved quantities of second-ordinary nonlinear coupled dynamics systems such as x=1（x，y），y=2（x，y），and the differential equations of integral factors and the general expression of conserved quantities are obtained. The Noether symmetry and Lie symmetry of the systems are also discussed. Finally，two conserved quantities of quartic anharminic oscillator are obtained by the extended Prelle-Singer method，and the symmetries of this system are discussed.
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