The application of differential characteristic set method to pseudo
Received:May 23, 2018  Revised:August 28, 2018
Key Word: Differential characteristic set   Differential division with remainder   Pseudo differential operator   Lax representation   Zakharov-Shabat equation.  
Fund ProjectL:University Science Foundation of China University of Labor Relations under (Grant No. 18YYJS017), and National Natural Science Foundation of China under (Grant No. 61271273).
Author NameAffiliationE-mail
Yifeng Jia China University of Labor Relations 
Dongliang Xiao China Agricultural University  
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      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 of a 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 which come from the general Lax equation and Zakharov-Shabat equation, are reduced, and the corresponding nonlinear evolution equation is obtained. The related programs are compiled in Mathematica computer algebra system,and Lax representation of some nonlinear evolution equations can be calculated with the aid of thecomputer.
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