具有高阶色散和立方-五次非线性项的薛定谔方程的孤立波的保持性  

Persistence of solitary waves of Schrödinger's equation withhigher⁃order dispersion and cubic⁃quintic nonlinear terms

作　　者：高晓涵 李威[1] GAO XiaoHan;LI Wei(College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029,China)

机构地区：[1]北京化工大学数理学院,北京100029

出　　处：《北京化工大学学报（自然科学版）》2023年第6期119-123,共5页Journal of Beijing University of Chemical Technology(Natural Science Edition)

摘　　要：研究了具有高阶色散项和立方-五次非线性项的薛定谔方程(NLSE)在扰动下孤立波解的保持性。通过行波变换将NLSE转化为平面动力系统,由Melnikov方法得到混沌阈值,通过分岔图、最大Lyapunov指数和Poincaré截面图验证了该系统存在Smale马蹄意义下的混沌,从而在参数选择时规避该区域来获得孤立波的保持区域。The persistence of solitary wave solitons in the nonlinear Schrödinger equation(NLSE)under disturb⁃ance has been investigated.The NLSE is transformed into a planar dynamical system by a traveling wave transfor⁃mation.The chaotic threshold is obtained by the Melnikov method.The period⁃doubling bifurcation diagram,the maximum Lyapunov exponent and the Poincarécross⁃section diagram are simulated to verify that there is chaos in the sense of a Smale horseshoe.The solitary wave holding region is obtained by avoiding the chaotic region when se⁃lecting parameters.

关 键 词：非线性薛定谔方程 MELNIKOV方法 同宿轨 混沌 

分 类 号：O193[理学—数学]