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藕合的AKNS方程的可积离散化Integrable Discretization of the Coupled AKNS
王佳, 张丽华, 李德生
AKNS方程, Hirota方法, 可积离散化, 孤子解AKNS Equation; The Hirota Method; Interable Discretization; Soliton Solution
《Advances in Applied Mathematics》, Vol.2 No.4, 2013-11-26
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.