(3+1)维广义非线性发展方程的双线性Backlund变换与精确解  

Bilinear Bäcklund Transform and Exact Solutions to a(3+1)-Dimensional Generalized Nonlinear Evolution Equation

作　　者：薛宇英 套格图桑[1,2,3] XUE Yuying;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2期173-182,共10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“非线性发展方程的贝克隆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Hirota双线性方法和试探函数法,研究一个(3+1)维广义非线性发展方程的双线性Backlund变换和精确解问题。用Hirota双线性法,构造(3+1)维广义非线性发展方程的双线性形式和双线性Backlund变换。基于双线性形式和双线性Backlund变换,利用试探函数法与符号计算系统Mathematica,获得(3+1)维广义非线性发展方程的多种精确解,包括呼吸波解、复合型解、Lump周期解和孤子解,并分析解的相互作用情况。The bilinear Bäcklund transformation and the exact solutions of a(3+1)dimensional generalized nonlinear development equation are studied based on the Hirota bilinear method and the trial function method in the paper.Firstly,the bilinear form and bilinear Bäcklund transformation of(3+1)⁃dimensional generalized nonlinear evolution equation are constructed by using Hirota bilinear method.Secondly,various exact solutions of(3+1)⁃dimensional generalized nonlinear evolution equation,including N⁃soliton solution,breather wave solution,compound solution,Lump periodic solution,Lump kink solution and soliton solution,are obtained by using trial function method and symbolic calculation system Mathematica based on bilinear form and bilinear Bäcklund transformation,and the interaction of the solutions is analyzed.

关 键 词：(3+1)维广义非线性发展方程 HIROTA双线性方法 BACKLUND变换 试探函数法 精确解 

分 类 号：O175.29[理学—数学]