How to find the conserved quantities of nonlinear discrete equations (Q2773069)

There is no systematic method of calculating the conserved quantities of the ordinary nonlinear difference equation, but discretization of integrable nonlinear ordinary differential equations gives some incomplete progress in this area. The authors give a method of finding conserved quantities of nonlinear ordinary difference equations. This method is based on the hypothesis that the conserved quantities are expressed by the ratio of two polynomials of independent variables. They explain the method by taking the discrete equation of motion of an anharmonic oscillator and a nonlinear difference equation of third order.