摘要
基于"AC=BD"的思想,通过假设的方法构造C-D对,可将非线性反应扩散方程,WBK方程以及Soliton Breaking方程转化为含参数多项式方程组,试图利用参数Groebner系统来求解相应的方程组,使用由Kapur等提出的KSW算法,并且和吴代数消元法进行了比较,可以看到KSW算法能提供不同参数约束下各分支解的信息.
The idea of"AC=BD"was applied to construct C-D pairs by the hypothetical method.The nonlinear reaction-diffusion equation,WBK equation and Soliton Breaking equation can be transformed into parametric polynomial equations.This paper tries to use the comprehensive Groebner systems to solve the corresponding equations.It uses the KSW algorithm proposed by Kapur,et al.,and compares it with Wu algebraic elimination method.It can see that the KSW algorithm can provide the information of solution in each branch under the different parametric constraints.
作者
张文哲
ZHANG Wen-zhe(Department of Science and Engineering,College of Arts and Science of Hubei Normal University,Huangshi 435109,China)
出处
《数学的实践与认识》
2021年第24期171-180,共10页
Mathematics in Practice and Theory
基金
湖北师范大学文理学院2020年校级科研项目(Ky202008)。
关键词
参数Groebner系统
假设构造法
偏微分代数方程
算法
comprehensive Groebner systems
hypothesis construction
partial differential algebraic equations
algorithm
