立方非线性Schr?dinger方程新精确解  

New exact solutions of cubic nonlinear Schr?dinger equations

作　　者：马志民[1] 孙峪怀[2] MA Zhi-min;SUN Yu-huai(Department of Basic Courses,Engineering and Technical College of Chengdu University of Technology,Leshan,614000,China;College of Mathematics and Software Science,Sichuan Normal University,Chengdu,610066,China)

机构地区：[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

出　　处：《量子电子学报》2019年第4期416-422,共7页Chinese Journal of Quantum Electronics

基　　金：四川省教育厅科研基金,15ZB0326;成都理工大学工程技术学院科研基金,C122016029~~

摘　　要：构造立方非线性Schrodinger方程精确解有助于方程相关物理背景的理解。利用广义exp[-φ(ξ)]-展开方法,借助符号计算系统-Maple,获得了立方非线性Schrodinger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其在光通信中的应用。可见此展开方法对求解数理问题中的非线性偏微分方程非常有效。Constructing exact solutions of cubic nonlinear Schrodinger equation is helpful to understand the relevant physical background of the equation.Some exact solutions of cubic nonlinear Schrodinger equation,such as hyperbolic function solutions,trigonometric function solutions and rational function solutions,are obtained by using the generalized exp[-χφ(ξ)]-expansion method and symbolic computation system-Maple.These new solutions contribute to the application in optical communications.It can be seen that this expansion method is very effective for solving nonlinear partial differential equations in mathematical physics problems.

关 键 词：非线性方程 精确解 广义exp[-φ(ζ)]-展开方法 立方非线性Schrodinger方程 

分 类 号：O175.2[理学—数学]