(2+1)维AKNS方程的初值扰动波及动力学行为  

Initial Value Perturbation Waves and Dynamical Behavior for(2+1)-D AKNS Equation

作　　者：康晓蓉[1] 鲜大权[1] 鲜骊珠 KANG Xiaorong;XIAN Daquan;XIAN Lizhu(School of Sciences,Southwest University of Science and Technology,Mianyang 621010,Sichuan,China;Chengdu University of Technology Sino-British Collaborative Education,Chengdu 610059,Sichuan,China)

机构地区：[1]西南科技大学理学院,四川绵阳621010 [2]成都理工大学中英合作办学,成都610059

出　　处：《西南科技大学学报》2021年第2期89-94,共6页Journal of Southwest University of Science and Technology

摘　　要：综合应用相平面分析法和初值扰动椭圆函数展开法研究(2+1)维AKNS方程。给出了方程行波闭轨和同异宿轨的存在性,获得了方程含时间任意函数初始解扰动的椭圆正弦函数精确解,分析了所获解结构在初值扰动下的三类特征,讨论了初值扰动波的局域激发几何结构。所获结果丰富了该方程的可积意义和动力学内涵。(2+1)-D AKNS equation was studied by the phase plane analysis and the elliptic function expansion method with initial perturbation in this work.The existence of closed orbit,homoclinic and heteroclinic orbit of the travelling wave for this equation were discussed,the elliptic sine function exact solutions with the initial perturbation of the time-dependent arbitrary function were obtained,and three types of characteristics of the obtained solutions structure under the initial value disturbance were analyzed.Also,the local excitation geometries of the traveling waves with perturbation were discussed.The results obtained enrich the integrability and mechanical connotation of the equation.

关 键 词：(2+1)维AKNS方程 行波初值扰动 相平面分析 椭圆函数展开法 局域激发结构 

分 类 号：O241.6[理学—计算数学]