The Application of Differential Characteristic Set Method to Pseudo Differential Operator and Lax Representation

Abstract:

      Differential characteristic set method is applied to the calculation of pseudo differential operators and Lax representation of nonlinear evolution equations. Firstly, differential characteristic set method and differential division with remainder are used for the calculation of inverse and extraction root of pseudo differential operator, such that the process is simplified since it is unnecessary to solve ordinary differential equation systems and substitute the solutions. Secondly, using differential characteristic set method, the nonlinear partial differential equation systems derived from the generalized Lax equation and Zakharov-Shabat equation, are reduced, and the corresponding nonlinear evolution equation is obtained. The related programs are compiled in Mathematica, a computer-based computer algebra system, and Lax representation of some nonlinear evolution equations can be calculated with the aid of the computer.