广义地球物理KdV方程的Lump波与扭结波相互作用解初值扰动行为  

Perturbation Behavior of Initial Value of Interaction Solution between Lump Wave and Kink Wave of Generalized Geophysical KdV Equation

作　　者：邱燕红 鲜大权[1] 田宝单[1] QIU Yanhong;XIAN Daquan;TIAN Baodan(School of Mathematics and Physics,Southwest University of Science and Technology,Mianyang Sichuan 621010,China)

机构地区：[1]西南科技大学数理学院,四川绵阳621010

出　　处：《大学数学》2024年第5期16-20,共5页College Mathematics

基　　金：四川教育厅科研基金项目(15ZB0113);达州市数学与金融研究中心项目(SCMF202304);西南科技大学龙山人才科研支持计划项目(18LZX622)。

摘　　要：针对一类广义地球物理KdV方程进行研究,利用Painleve分析思想构造了一个包含初始常数解的双线性变换,并应用拟设函数法得到两类与初值有关的Lump波与周期波、扭结波相互作用的显式精确解.此外,根据包含初始常数解u 0扰动的解的结构得到u 0的两个分叉点.最后,在一定参数条件下,利用数学软件对所得Lump波与周期波相互作用模式、Lump波与扭结波相互作用模式进行了绘图展示.结果表明:方程初始常数解对广义地球物理KdV方程的发展性态具有明显的扰动特征.A class of generalized geophysical KdV equation is studied in this paper.By using the method of Painléve analysis,a bilinear transformation with the initial steady-state constant solution is constructed.Furthermore,the explicit and exact solutions of the interaction of two kinds of Lump waves related to initial values with periodic waves and kink waves are obtained by using the hypothetical function method.In addition,according to the structure of the perturbation solution,two bifurcation points of the initial disturbance solution are also obtained.Finally,the interaction modes of Lump wave and periodic wave,Lump wave and kink wave are obtained and displayed by mathematical software under certain parameters.The results show that the initial steady-state solutions of the equation have obvious disturbance characteristics on the development of the generalized geophysical KdV equation.

关 键 词：广义地球物理KdV方程 双线性法 初值扰动 Lump波 扭结波 

分 类 号：O175.29[理学—数学]