非稳定非线性薛定谔方程的马尔钦科方程

数学物理学报 ›› 1999, Vol. 19 ›› Issue (4): 461-466.

非稳定非线性薛定谔方程的马尔钦科方程

（武汉大学物理系　广州市桂花岗广州师范学院物理系　广州５１０４００）

（暨南大学物理系　暨南５１０６３２

出版日期:1999-11-01 发布日期:1999-11-01

machenko equation of the unstable nonlinear schrodinger equation

(Department of Physics, Wuhan University, Wuhan 430072)

(Department of Physics, Jinan University, Jinan 510632)

Online:1999-11-01 Published:1999-11-01

摘要/Abstract

摘要：

该文基于对非稳定非线性薛定谔方程作反散射变换得到的Zakharov-Shabat方程，直接对积分核作变换，导出马尔钦科方程.得到的马尔钦科方程在形式上与一般非线性薛定谔方程得到的一样简单明了，且不存在逆变换的自洽困难.

关键词: 　非线性薛定方程, 反散射, 弥钦科方程．

Abstract:

The unstable nonlinear Schrodinger(NLS) equaiton is solved by the inverse scattering transform. A transformation is made directly to the integral nuclei of the ZakharovShabat equation, and the Marchenko equation is thus derived. It is found that the Marchenko equation is as simple as that of a usual NLS equation , and the Zakharov-Shabat equation can be found from the Machenko equation by the inverse transformation.

Key words: 　ＮＬＳｅｑｕａｔｉｏｎ, ＩｎｖｅｉｓｅＳｃａｔｔｅｒｉｎｇｔｒａｎｓｆｏｒｍ, Ｍａｒｃｈｅｎｋｏｅｑｕａｔｉｏｎ．

中图分类号:

　３５Ｑ

陈芝得陈向军. 非稳定非线性薛定谔方程的马尔钦科方程[J]. 数学物理学报, 1999, 19(4): 461-466.

Chen Zhide Chen Xiangjun. machenko equation of the unstable nonlinear schrodinger equation[J]. Acta mathematica scientia,Series A, 1999, 19(4): 461-466.