(3+1)维Jimbo-Miwa方程的分离变量解与相互作用  

The Variables Separation Solutions and Their Interaction of the(3+1)Dimensional Jimbo-Miwa Equation

作　　者：伊丽娜[1] 扎其劳[1,2,3] 套格图桑 Yiina;Zhaqiao;Taogetusang(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematical Science,Hohhot 010022,China;Key Laboratory of Infinite Dimensional Hamiltonian System and Its Algorithm Application,Ministry of Education,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022 [3]无穷维哈密顿系统及其算法应用教育部重点实验室,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学版）》2024年第3期313-320,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目“在周期背景上的怪波及其相关问题研究”(12361052);内蒙古自治区青年科技发展资助项目“应用数学”(NMGIRT2414);内蒙古师范大学基本科研业务费资助项目“支持一流科技领军人才和创新团队建设”(2022JBZD011),“应用数学创新团队建设项目”(2022JBTD007)。

摘　　要：构造(3+1)维Jimbo-Miwa(J-M)方程由任意函数组成的分离变量解,并分析解的相互作用。通过一种函数变换,将(3+1)维Jimbo-Miwa(J-M)方程的求解问题转化为常微分方程和非线性代数方程组的求解问题。借助符号计算系统Mathematica求出非线性代数方程组的解。用常微分方程的解与非线性代数方程组的解,构造(3+1)维Jimbo-Miwa(J-M)方程由任意函数组成的分离变量解。根据函数的任意性,通过图像分析了解其相互作用。The variables separation solutions composed of arbitrary function of the(3+1)dimensional Jimbo Miwa(J-M)equation are constructed and the interaction of solutions is analyzed in the paper.To solve the(3+1)dimensional Jimbo Miwa(J-M)equation,the solutions to the(3+1)dimensional are firstly transformed into the solutions to ordinary differential equations and nonlinear algebraic equation systems through a kind of function transformation,and then the solutions of nonlinear algebraic equations are solved by using the symbolic computing system Mathematica.The solutions of the(3+1)dimensional Jimbo Miwa(J-M)equation are constructed from solutions of ordinary differential equations and nonlinear algebraic equations,which are separated variable solutions composed of arbitrary function.The interaction of the solutions is analyzed through image analysis technique according to the arbitrariness of the function.

关 键 词：函数变换 (3+1)维Jimbo-Miwa方程 分离变量解 相互作用 

分 类 号：O175.29[理学—数学]