Jimbo-Miwa-Like方程的Lax可积性研究  

Lax-Integrability and Related Problems of Jimbo-Miwa-Like Equation

作　　者：张晓乐 套格图桑[1,2,3] ZHANG Xiaole;Taogetusang(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematics,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（自然科学汉文版）》2024年第1期27-37,共11页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：内蒙古自治区自然科学基金资助项目“非线性发展方程的求解与可积性问题研究”(2020LH01008);内蒙古师范大学基本科研业务费专项资金资助项目“非线性发展方程的B?cklund变换与无穷守恒律问题研究”(2022JBZD011);内蒙古师范大学研究生科研创新基金资助项目“非线性发展方程的可积性与相关问题研究”(CXJJB23009)。

摘　　要：基于双Bell多项式方法,将Jimbo-Miwa-Like方程化为双线性形式,运用Bell多项式的相关性质,构造出方程的双Bell多项式B?cklund变换、双线性B?cklund变换、Lax对、无穷守恒律和孤子解。运用试探函数法和符号计算软件Mathematica获得方程的复合型解,并选取适当的参数,绘制一部分精确解的图像来说明性质。The Jimbo-Miwa-Like equation is transformed into bilinear form based on the Bell-polynomial method,and double Bell polynomial Bäcklund transformation,bilinear Bäcklund transformation,Lax pair,infinite conservation law and solitons of the equation are derived through symbolic computation by using the relevant properties of Bell-polynomial.Then,the complex solutions are obtained by applying the trail function method and symbolic calculation software Mathematica,and some of graphs for exact solutions are made to illustrate their properties through selecting the appropriate parameters.

关 键 词：Bell多项式方法 B?cklund变换 LAX对 无穷守恒律 试探函数法 

分 类 号：O175.29[理学—数学]