摘要
通过行波变换将一类非线性薛定谔方程及其推广形式转化为常微分方程动力系统,求出其奇点,并讨论其类型;计算出系统的哈密尔顿量,并运用Maple软件,画出了系统的奇点和相图;求出动力系统的解,并回代求出非线性偏微分方程及其推广形式的精确行波解.
To solve the nonlinear Schr6dinger equation, the former had constructed the rogue wave solutions,but they did not give the exact travelling wave solution of it. In this paper, we chance from the focusing nonlinear Schr6dinger equation and its promotion form to dynamical systems by reduce traveling wave system,and discuss the types of the singular points of system after we get the singular points;Then,we divide the system and obtain a Hamilton system. With the help of Maple software,it shows the singular points in the phase portraits clearly;Finally,we take the solutions of dynamical systems back to the focusing nonlinear Schr6dinger equation and its promotion form. There are two forms exact traveling wave solutions of NLSE and its promo tion form,and it describes the solutions with three-dimensional graph visually.
出处
《云南师范大学学报（自然科学版）》
2015年第6期39-44,共6页
Journal of Yunnan Normal University:Natural Sciences Edition
基金
云南省教育厅高等学校教学改革研究计划资助项目(2012019)
关键词
非线性薛定谔方程
推广形式
动力系统
哈密尔顿量
行波解
Dynamical systems
Promotion form
Hamiltonian
Singular points
Phase portraits
Traveling wave solutions
