一类动力学中非线性偏微分方程解的研究与分析  

Research and Analysis of Solutions of a Class of Nonlinear Partial Differential Equations in Dynamics

作　　者：赵贞 张明霞 庞晶[1] 额尔敦布和 ZHAO Zhen;ZHANG Ming-xia;PANG Jing;ErdunBuhe(College of Science,Inner Mongolia University of Technology,Hohhot 010051,China;Academic Affairs office,Hohhot Minzu College,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院,内蒙古呼和浩特010051 [2]呼和浩特民族学院教务处,内蒙古呼和浩特010051

出　　处：《数学的实践与认识》2023年第5期211-225,共15页Mathematics in Practice and Theory

摘　　要：通过Ibragimov新守恒定理的基本思想,构造了动力学Drinfel’d-Sokolov-Wilson(DSW)方程的局部守恒定律.并且利用Hirota双线性形式推导出该方程的双线性Backlund变换,在双线性Backlund变换的基础上,获得该方程的行波解.然后构造DSW方程的正四次函数、二次函数及指数函数所组合的形式解,另外构造了正四次函数、二次函数、三角函数和双曲函数组合的形式解,通过计算求解出DSW方程相应的高阶Lump解与Kink解、高阶Lump解与周期波解的相互作用解,同时验证了该方程解的存在性.Based on the basic idea of Ibragimov's new conservation theorem,the local conservation law of dynamic Drinfel'd-Sokolov-Wilson(DSW)equation is constructed.The bilinear Backlund transformation of the equation is derived by Hirota bilinear form.On the basis of the bilinear Backlund transformation,the traveling wave solution of the equation is obtained.Then DsW equations are four function,quadratic function and exponential function combination in the form of a solution,the other is constructed four function,quadratic function,trigonometric function and hyperbolic function composition in the form of a solution,by calculating the DSW equation,the corresponding high order Lump solutions,Kink solutions and higher order Lump solutions and periodic wave solutions of the interaction,and verified the party The existence of solutions.

关 键 词：DSW方程 Ibragimov新守恒定理 双线性B?cklund变换 相互作用解 

分 类 号：O175.29[理学—数学]