立方非线性Schr\"{o}dinger方程新精确解

量子电子学报 ›› 2019, Vol. 36 ›› Issue (4): 416-422.

立方非线性Schr\"{o}dinger方程新精确解

马志民¹,孙峪怀²

1成都理工大学工程技术学院基础部，四川乐山 614000； 2四川师范大学数学与软件科学学院，四川成都 610066

收稿日期:2018-12-03 修回日期:2019-01-06 出版日期:2019-07-28 发布日期:2019-07-11
作者简介:马志民（1984-），山西大同，硕士，讲师，主要从事研究方向为孤立子与可积系统理论及其应用方面的研究.E-mail：mazhimin9162@163.com
基金资助:
Supported by Scientific Research Foundation of Engineering and technical College of Chengdu University of Technology (成都理工大学工程技术学院青年科学基金, C122016029), Scientific Research Foundation of the Education Department of Sichuan Province, China (四川省教育厅科研基金,15ZB0326)

The new exact solutions of cubic nonlinear schr\"{o}dinger equations

MA Zhi-min 1，*， SUN Yu-huai 2

1 Department of Basic Courses，Engineering and Technical College of Chengdu University of Technology，Leshan，614000， China; 2 College of Mathematics and Software Science，Sichuan Normal University，Chengdu，610066，China

Received:2018-12-03 Revised:2019-01-06 Published:2019-07-28 Online:2019-07-11

摘要/Abstract

摘要： 构造立方非线性Schr\"{o}dinger方程精确解有助于方程相关物理背景的理解。利用广义exp(-\phi(\xi))-展开方法，借助符号计算系统-Maple，获得了立方非线性Schr\"{o}dinger方程的多种精确解，如双曲函数解、三角函数解和有理函数解，其中包括一些新的结果。这些新的结果有助于在光通信中的应用。同时，可见此展开方法对求解数理问题中的非线性偏微分方程是非常有效的。

关键词: 非线性方程；精确解；广义 -展开方法；立方非线性Schrö, dinger方程；光通信；符号计算

Abstract: Constructing exact solutions of cubic nonlinear schr\"{o}dinger equation will be better help us to understand the physical phenomenon of cubic schr\"{o}dinger equation. Generalized exp(-\phi(\xi))-expansion method is given here. Based on this method and the aid of symbolic computation system-Maple，new exact solutions of cubic nonlinear schr\"{o}dinger equation are obtained. These solutions include hyperbolic function solutions， trigonometric function solutions and rational function solutions.As a result, many new exact solutions are obtained. New solutions can be used in optical communications. It has been shown that this method provides a powerful mathematical tool for solving nonlinear partial differential equations in mathematical physics problems.

Key words: nonlinear equations, exact solutions, generalized -expansion method, cubic nonlinear schrödinger equations, optical communications, symbolic computation

中图分类号:

O175.2

马志民1，*，孙峪怀2，. 立方非线性Schr\"{o}dinger方程新精确解[J]. 量子电子学报, 2019, 36(4): 416-422.

MA Zhi-min 1，*， SUN Yu-huai 2. The new exact solutions of cubic nonlinear schr\"{o}dinger equations[J]. Chinese Journal of Quantum Electronics, 2019, 36(4): 416-422.

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