贾屹峰,肖东亮.微分特征列法在拟微分算子和Lax表示中的应用[J].数学研究及应用,2019,39(2):196~220
微分特征列法在拟微分算子和Lax表示中的应用
The Application of Differential Characteristic Set Method to Pseudo Differential Operator and Lax Representation
投稿时间:2018-05-23  修订日期:2018-09-05
DOI:10.3770/j.issn:2095-2651.2019.02.008
中文关键词:  微分特征列  微分带余除法  拟微分算子  Lax表示  Zakharov-Shabat方程
英文关键词:differential characteristic set  differential division with remainder  pseudo differential operator  Lax representation  Zakharov-Shabat
基金项目:中国劳动关系学院院级科研项目(Grant No.18YYJS017),国家自然科学基金(Grant No.61271273).
作者单位
贾屹峰 中国劳动关系学院数学与计算机教学部, 北京 100048 
肖东亮 中国农业大学信息与电子工程学院, 北京 100083 
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中文摘要:
      微分特征列法用于拟微分算子和非线性发展方程Lax表示的计算.首先,利用微分特征列法和微分带余除法计算拟微分算子的逆和方根,由于不必求解常微分方程组,并将解代入,因此,使得计算得以简化.其次,利用微分特征列法,约化从广义Lax方程和Zakharov-Shabat推出的非线性偏微分方程,并得到相应的非线性发展方程.在Mathematica计算机代数系统上,编写了相关程序,从而可以利用计算机辅助完成一些非线性发展方程Lax表示的计算.
英文摘要:
      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.
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