Bell多项式在变系数Gardner-KP方程中的应用

J4 ›› 2016, Vol. 33 ›› Issue (6): 671-679.

Bell多项式在变系数Gardner-KP方程中的应用

张小媛,许晓革,孟祥花

1 北京物资学院信息学院, 北京 101149; 2 北京信息科技大学理学院, 北京 100192

收稿日期:2015-10-09 修回日期:2016-03-31 出版日期:2016-11-28 发布日期:2016-11-28
通讯作者: 许晓革(1966-)，女，博士，教授，研究方向为非线性分析及其应用。 E-mail:xxg@bistu.edu.cn
基金资助:
国家自然科学基金项目(61471406); 国家自然科学基金项目(11401031)

Application of Bell polynomials in variable-coefficient Gardner-KP equation

XU Xiaoge, ZHANG Xiaoyuan, MENG Xianghua

1 School of Information, Beijing Wuzi University, Beijing 101149, China; 2 School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China

Received:2015-10-09 Revised:2016-03-31 Published:2016-11-28 Online:2016-11-28

摘要/Abstract

摘要： 借助于Bell多项式，构造了变系数Gardner-KP方程的双线性形式。利用摄动展开法得到了方程的单孤立波解、双孤立波解及多孤立波解，并对单孤立波的特征进行了分析。同时，根据双线性方程，推导了变系数Gardner-KP方程带有参数的Bell多项式型和双线性形式的B?cklund变换。

关键词: 基础光学；Bell多项式；变系数Gardner-KP方程；孤立波解；B?cklund 变换

Abstract: Using the Bell polynomials, Hirota bilinear form of variable-coefficient Gardner-KP equation is constructed. With the perturbation expansion method, single soliton solution, two- soliton solution and multiple soliton solution of the equation are obtained and the characteristic of the single solitary wave is analyzed. Meanwhile, the B?cklund transformations with parameters of the Gardner-KP equation in Bell polynomial and bilinear form are derived according to it’s bilinear equation.

Key words: basic optics; Bell polynomials; variable-coefficient Gardner-KP equation; solitary wave solution; B?cklund transformation

中图分类号:

O175.2

张小媛许晓革孟祥花. Bell多项式在变系数Gardner-KP方程中的应用[J]. J4, 2016, 33(6): 671-679.

XU Xiaoge, ZHANG Xiaoyuan, MENG Xianghua. Application of Bell polynomials in variable-coefficient Gardner-KP equation [J]. J4, 2016, 33(6): 671-679.

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