The extended Prelle-Singer method for the conserved quantities of second-ordinary nonlinear coupled dynamics systems and their symmetries

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.