一个高维非线性方程的三波解  

The Three-Wave Solutions for a High Dimensional Nonlinear Equation

作　　者：郭婷婷 GUO Tingting(Department of Mathematics Teaching and Research,Shanxi Vocational University of Engineering Science and Technology,Taiyuan 030619,China)

机构地区：[1]山西工程科技职业大学数学教学研究部,山西太原030619

出　　处：《太原学院学报（自然科学版）》2021年第2期81-86,共6页Journal of TaiYuan University:Natural Science Edition

基　　金：山西大学商务学院科研基金(2020040)。

摘　　要：为更好地理解孤子理论中孤波的演化,基于拟设法来研究(3+1)维非线性偏微分方程,用该方法构造比以往孤波解更具一般形式的三波解。借助双线性算子,将(3+1)维非线性波模型转化为双线性方程,依据推广的三波理论,假设出包含一些未知参数的双线性方程的解,在符号计算的帮助下,求解代数方程系统,得到双线性方程的四类解,成功构造出(3+1)维非线性微分方程的精确解,并图形化展示出所得解,借助六幅解的样图可以研究三波解的物理性态。这种方法也可用于求解其他数学物理非线性波动方程。In order to better understand the evolution of soliton waves in the soliton theory,the article investigates into the(3+1)-dimensional nonlinear partial differential equation based on the ansatz method,which can be used to constuct three-wave solutions with more generalized forms,than the original soliton wave solutions.The(3+1)-dimensional nonlinear wave model is converted into the bilinear equation by using bilinear operator.According to the extended three wave approach,the solutions of bilinear equation involving some unknown parameters are supposed,the algebraic equation system is solved with the help of symbolic computation,four kinds of solutions of bilinear equation are presented,exact solutions of the(3+1)-dimensional nonlinear differential equation are successfully established and some obtained results are exhibited graphically.The physical behaviors of three wave solutions are discussed through the figures for six sample solutions.This method can also be applied to solve other nonlinear wave equations arising from mathematical physics.

关 键 词：三波解 双线性算子 高维非线性方程 符号计算 拟设法 

分 类 号：O129.35[理学—数学]