广义带导数的非线性Schrödinger方程的动态分析和精确解

杨娜; 陈龙伟; 熊梅

doi:10.21656/1000-0887.380302

广义带导数的非线性Schrödinger方程的动态分析和精确解

doi: 10.21656/1000-0887.380302

云南财经大学统计与数学学院, 昆明 650221

基金项目: 国家自然科学基金(11761075)

详细信息

作者简介:
杨娜(1991—)，女，硕士(E-mail: 513327775@qq.com);陈龙伟(1967—)，男，博士(通讯作者. E-mail: tc715@sina.com).

中图分类号: O357.41
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- 文章访问数: 1010
- HTML全文浏览量: 90
- PDF下载量: 505
- 被引次数: 0
出版历程
- 收稿日期: 2017-12-05
- 修回日期: 2018-01-17
- 刊出日期: 2018-10-01

Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative

School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, P.R.China

Funds: The National Natural Science Foundation of China(11761075)

摘要

摘要: 利用动力系统方法，针对广义带导数的非线性Schrödinger方程的精确解问题进行研究分析.采用行波变换，将其化为常微分方程动力系统；计算出该方程动力系统的首次积分，讨论了系统在不同参数条件下的奇点与相图，得到对应的精确解，包括孤立波解、周期波解、扭结波解和反扭结波解.运用数值模拟的方法，对方程的光滑孤立波解和周期波解等进行了数值模拟。分析计算获得的结果完善了相关文献已有的研究成果.
- 非线性Schrödinger方程 /
- 动力系统 /
- 孤立波解
Abstract: With the dynamic system method, the qualitative performance and the exact solution of the general nonlinear Schr?dinger equation with derivative were studied. Through the traveling wave transformation, the corresponding ordinary differential equation was deduced and the first integral was calculated. Under different parameter space conditions, the bifurcations of the general nonlinear Schrödinger equation with derivative were investigated, and the exact traveling wave solutions were obtained, such as solitary solutions, periodic solutions as well as kink and anti-kink solutions. The solitary wave solutions were considered through numerical simulation. The results show that the present findings improve the related previous conclusions.
- nonlinear Schr?dinger equation /
- dynamic system /
- solitary wave solution

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参考文献(15)

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广义带导数的非线性Schrödinger方程的动态分析和精确解

doi: 10.21656/1000-0887.380302

作者简介:
杨娜(1991—)，女，硕士(E-mail: 513327775@qq.com);陈龙伟(1967—)，男，博士(通讯作者. E-mail: tc715@sina.com).

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Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative

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广义带导数的非线性Schrödinger方程的动态分析和精确解

doi: 10.21656/1000-0887.380302

作者简介: 杨娜(1991—)，女，硕士(E-mail: 513327775@qq.com);陈龙伟(1967—)，男，博士(通讯作者. E-mail: tc715@sina.com).

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出版历程

Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative

计量

出版历程

目录

作者简介:
杨娜(1991—)，女，硕士(E-mail: 513327775@qq.com);陈龙伟(1967—)，男，博士(通讯作者. E-mail: tc715@sina.com).