AAM  >> Vol. 2 No. 4 (November 2013)

    藕合的AKNS方程的可积离散化
    Integrable Discretization of the Coupled AKNS Equation

  • 全文下载: PDF(165KB) HTML    PP.159-164   DOI: 10.12677/AAM.2013.24021  
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作者:  

王 佳,张丽华,李德生:沈阳师范大学数学与系统科学学院,沈阳

关键词:
AKNS方程Hirota方法可积离散化孤子解AKNS Equation; The Hirota Method; Interable Discretization; Soliton Solution

摘要:

本文主要研究了藕合的二阶AKNS方程的可积离散化。首先对藕合的二阶AKNS方程的半离散双线性导数方程运用Hirota方法和Maple求出了其新的N-孤子解;然后通过对半离散的双线性导数方程中的时间变量进行离散化,得到全离散的双线性导数方程并对其进行了求解;最后通过适当的变换得出差分差分AKNS方程。
>This paper mainly studied the integrable discretization of the second order coupled AKNS equation. First of all, some new N soliton solutions of the semi-discrete double linear derivative equation of the second order coupled AKNS equation are got by using the Hirota method and Maple. Then, the full discrete bilinear derivative equation is obtained through the method of discrete time of the semi-discrete double linear deriva- tive equation and its N soliton solutions are found out. Finally, the difference-difference AKNS equation is obtained by an appropriate transformation.

文章引用:
王佳, 张丽华, 李德生. 藕合的AKNS方程的可积离散化[J]. 应用数学进展, 2013, 2(4): 159-164. http://dx.doi.org/10.12677/AAM.2013.24021

参考文献

[1] Bi, J.-B., Sun, Y.-P. and Chen, D.-Y. (2006) Soliton solutions for nonisospectral AKNS equation by Hirota method. Communications in Theo- retical Physics (Beijing, China), 45, 398-400.
[2] Sun, Y.-P. and Chen, D.-Y. (2006) Integrable couplings and new exact solutions for the nonisospectral AKNS equation. International Journal of Modern Physics B, 20, 925-935.
[3] 姚玉芹 (2007) (2 + 1)维孤子方程的精确解与可积系统. 上海大学, 上海.
[4] 季杰 (2007) 若干离散可积系统的对称与反向AKNS方程的精确解. 上海大学, 上海.
[5] 陈守婷 (2011) 半离散AKNS系统的对称与代数结构. 上海大学, 上海.
[6] 丁大军 (2011) 一类孤子方程的可积离散化.浙江师范大学, 浙江.
[7] 孙玉娟, 丁琦, 梅建琴, 张鸿庆 (2013) D-AKNS方程的代数几何解. 数学物理学报, 2, 276-284.
[8] Hirota, R. (2000) Discretization of coupled modified KdV equations. Chaos, Solitons and Fractals, 11, 77-84.