具有高阶色散和立方-五次非线性项的薛定谔方程的精确解  

Exact solutions for the Schrödinger equation with higher-order dispersive terms and cubic-quintic nonlinear terms

作　　者：买欣蕾 李威[1] MAI XinLei;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）》2021年第3期114-120,共7页Journal of Beijing University of Chemical Technology(Natural Science Edition)

摘　　要：研究描述超短光脉冲在光纤中传播的一类薛定谔方程。采用代入法将非线性薛定谔方程简化为Hamilton系统,利用动力系统的分岔理论讨论系统在不同参数条件下的平衡点与相图,并获得对应的孤立波解、扭结波解和周期波解等行波解。A Schrödinger equation describing the propagation of ultrashort optical pulses in optical fibers has been investigated.The nonlinear Schrödinger equation is simplified into a Hamilton system by a substitution method,and then the equilibrium point and phase portrait of the system under different parameter conditions are discussed using the theory of bifurcations for dynamical systems.The corresponding traveling wave solutions such as solitary wave solutions,kink wave solutions,and periodic wave solutions are thus obtained.

关 键 词：非线性薛定谔方程 动力系统 行波解 

分 类 号：O193[理学—数学]