| Bell多项式在变系数Gardner-KP方程中的应用 |
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| 引用本文： | 许晓革,张小媛,孟祥花.Bell多项式在变系数Gardner-KP方程中的应用[J].量子电子学报,2016,33(6):671-679. |
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| 作者姓名： | 许晓革 张小媛 孟祥花 |
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| 作者单位： | 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 |
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| 基金项目： | Supported by National Natural Science Foundation of China(国家自然科学基金 |
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| 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。
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| 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 |
| 收稿时间： | 2015-10-09 |
| 修稿时间： | 2016-03-31 |
Application of Bell polynomials in variable-coefficient Gardner-KP equation |
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| XU Xiaoge,ZHANG Xiaoyuan,MENG Xianghua.Application of Bell polynomials in variable-coefficient Gardner-KP equation[J].Chinese Journal of Quantum Electronics,2016,33(6):671-679. |
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| Authors: | XU Xiaoge ZHANG Xiaoyuan MENG Xianghua |
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| Affiliation: | 1 School of Information, Beijing Wuzi University, Beijing 101149, China;
2 School of Applied Science, Beijing Information Science and Technology University,
Beijing 100192, China |
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| 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. |
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| Keywords: | nonlinear equation Bell polynomials variable-coefficient Gardner-KP equation solitary wave solution B(a)cklund transformation |
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