一维对称正则长波方程的动力学行为及行波解的分类  

Dynamic Behavior of One-dimensional Symmetric Regular Long Wave Equation and Classification of Traveling Wave Solutions

作　　者：彭丽[1] 张长浩 PENG Li;ZHANG Chang-hao(Shandong University of Science and Technology,Pubic Course Department,Taian 271019,China;Beijing Information Science,Technology University,Beijing 100192,China)

机构地区：[1]山东科技大学公共课教学部,山东泰安271019 [2]北京信息科技大学理学院,北京100192

出　　处：《数学的实践与认识》2021年第24期246-252,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金面上项目(11971067);山东科技大学群星计划项目(QX2020M86)。

摘　　要：利用平面动力系统的分岔理论和方法,定性地分析了一维对称正则长波方程的动力学行为及其精确解的分类,获得了该方程的行波系统在不同参数条件下的轨线图.通过对所有的轨道进行分析,结合解的分类图,得到了该方程行波解的显式表达式.这些解包括有理解、孤立波解、爆破解、周期解等,展示了由参数变化引起的分岔现象,并丰富了一维对称正则长波方程精确解的类型.Based on the bifurcation theory and method of planar dynamical system,the onedimensional symmetric regularized-long-wave nonlinear equation is qualitatively analyzed,and the orbits of the traveling wave system of the equation under different parameters are obtained.By analyzing all orbits and combining with the classification diagram of the solutions of the equation,the explicit expressions of traveling wave solutions of the equation are obtained.These solutions include algebraic solution,solitary wave solutions,unbounded solutions and periodic solutions,which show the bifurcation phenomenon caused by parameter changes and enrich the types of solutions.

关 键 词：分岔理论 对称正则长波方程 行波解 孤立波解 解的分类 

分 类 号：O175[理学—数学]