一族耦合Kaup-Newell方程及其相伴可积分解  

A Hierarchy of Coupled Kaup-Newell Equations and the Associated Integrable Decomposition

作　　者：蒋巧云[1] 袁邢华[1] 吕效国[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《数学的实践与认识》2013年第16期213-218,共6页Mathematics in Practice and Theory

基　　金：南通大学自然科学基金(10Z010)

摘　　要：通过介绍一个含四个位势的4×4矩阵谱问题,得到一个新的非线性发展方程族,其中较有意义的一个方程是耦合Kaup-Newell方程.利用迹恒等式,得到了它的双哈密顿结构.在某个约束条件下,通过特征值问题的非线性化方法,得到了Liouville意义下耦合Kaup-Newell方程新的可积分解.By introducing a 4 ~ 4 matrix spectral problem with four potentials, a hierarchy of nonlinear evolution equations are derived, an interesting equation in the hierarchy is a coupled Kaup-Newell equation. The 2-Hamiltonian structures are presented with the aid of the trace identity. Through the nonlinearization of eigen value problems and an additional constraint, a new integrable decomposition of the coupled Kaup-Newell equation is presented in the sense of Liouville.

关 键 词：耦合Kaup—Newell方程 Lax对非线性化 可积分解 

分 类 号：O175.29[理学—数学]