广义(2+1)维Hirota-Satsuma-Ito方程的分岔理论与动力学分析  

Bifurcation and Dynamical Analysis of(2+1)Dimensional Generalized Hirota-Satsuma-Ito Equation

作　　者：李海丽 吴娟娟 LI Hai-li;WU Juan-juan(Beijing Information Science&Technology University,Beijing 100096,China)

机构地区：[1]北京信息科技大学理学院,北京100096

出　　处：《数学的实践与认识》2020年第15期253-261,共9页Mathematics in Practice and Theory

基　　金：北京市教师队伍建设“长城学者”项目(CIT&TCD20180325);国家自然科学基金面上项目(11971067);北京信息科技大学学校科研基金(5221710907)。

摘　　要：主要研究了广义(2+1)维的Hirota-Satsuma-Ito(HSI)方程行波解的分岔及其动力学行为.基于行波变换,文章推导出(2+1)维广义HSI方程对应的平面动力系统.通过对平面动力系统参数不同取值的讨论,确定系统的奇点的个数和类型,得到了动力系统的轨线图.根据系统分岔情况,求解了广义的(2+1)维HSI方程相对应动力系统的不同轨线所有行波解的解析表达式,并作图展示了三类孤立波—bell型孤立波,暗孤立波和线周期波的具体性状.In this paper,the bifurcation and dynamics of the traveling wave solutions of the(2+1)-dimensional generalized Hirota-Satsuma-Ito equation are studied.Based on the traveling wave transform,we derive the planar dynamical system corresponding to the generalized(2+1)-dimensional HSI equation.According to the discussion of the parameters of the planar dynamic system,the number and types of singularities of the system are determined,and the trajectory diagrams of the power system are obtained.Analytical solutions of three types of solitary waves,bell-shaped solitary waves,dark solitary waves and periodic waves,are studied,which are corresponding to different orbits bifurcated from dynamical system of the(2+1)-dimensional HSI equations.

关 键 词：孤立子 分岔理论 幂零奇点 行波解 线周期波 

分 类 号：O175.29[理学—数学]