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(2+1)维色散长波方程的新孤子解及其演化

New Soliton Solutions and Soliton Evolvements for(2+1)-Dimensional Dispersive Long Wave Equation

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摘要

借助Mathematica数学软件进行符号计算, 先将由G′/G展开法改进得到的F/G展开法进行拓展, 然后结合变量分离法得到一系列高维非线性发展方程的精确解。以(2+1)维色散长波方程为例, 利用F/G展开法构造精确解的方法是将原来的行波变换扩展为任意函数的变换, 行波变换则成为任意函数变换的特例, 从而得到(2+1)维色散长波方程的非行波解。通过选择适当的函数, 分别构造出(2+1)维色散长波方程的亮暗dromion解(局域解)和周期孤立波解。研究了设定参数下亮暗dromion解随时间的传播情况, 以及周期孤立波解随时间的演化情况。

Abstract

With the help of Mathematica symbol calculation software, we extend the F/G expansion method improved by the G′/G expansion method and obtain exact solutions of a series of high dimensional nonlinear evolution equations by combining the variable separation method. Taking a (2+1)-dimensional dispersive long wave equation as an example, constructing the exact solutions by F/G expansion method is to extend the original traveling wave transform to any function transform, in which the traveling wave transform is only a special case of this any function transform. Then the non-traveling wave solutions of the (2+1)-dimensional dispersive long wave equation are obtained. By choosing the appropriate function, we can construct (2+1)-dimensional bright dromion solution and periodic solitary wave solution of the dispersion long wave equation. Then we study the propagation of the bright dromion solution with time and the evolution of the periodic solitary wave solution over time further.

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中图分类号:O175.2

DOI:10.3788/lop55.011901

所属栏目:非线性光学

基金项目:贵州省教育厅青年科技人才成长项目(黔教合KY字[2016]304)、贵州省卓越教师教育培养计划(数学与应用数学[2015]25)

收稿日期:2017-07-16

修改稿日期:2017-08-13

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作者单位    点击查看

杨娟:凯里学院理学院, 贵州 凯里 556000
冯庆江:凯里学院理学院, 贵州 凯里 556000

联系人作者:杨娟(hnyangjuan1982@126.com)

备注:杨娟(1982-), 女,硕士, 副教授, 主要从事非线性数学物理方程方面的研究。E-mail: hnyangjuan1982@126.com

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引用该论文

Yang Juan,Feng Qingjiang. New Soliton Solutions and Soliton Evolvements for(2+1)-Dimensional Dispersive Long Wave Equation[J]. Laser & Optoelectronics Progress, 2018, 55(1): 011901

杨娟,冯庆江. (2+1)维色散长波方程的新孤子解及其演化[J]. 激光与光电子学进展, 2018, 55(1): 011901

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