The Application of Differential Characteristic Set Method to Pseudo Differential Operator and Lax Representation
Received:May 23, 2018  Revised:September 05, 2018
Key Word: differential characteristic set   differential division with remainder   pseudo differential operator   Lax representation   Zakharov-Shabat
Fund ProjectL:Supported by the University Science Foundation of China University of Labor Relations (Grant No.18YYJS017) and the National Natural Science Foundation of China (Grant No.61271273).
 Author Name Affiliation Yifeng JIA Teaching Department of Mathematics and Computer, China University of Labor Relations, Beijing 100048, P. R. China Dongliang XIAO College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, P. R. China
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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.
Citation:
DOI:10.3770/j.issn:2095-2651.2019.02.008