一类广义NLS-MKdV方程族及其双哈密顿结构  

A Classical Generalized NLS-MKdV Hierarchy and Its Bi-Hamiltonian Structure with Self-consistent Sources

作　　者：董凤娇[1] 胡贝贝 DONG Fengjiao;HU Beibei(School of Computer and Information Engineering,Chuzhou University,Chuzhou 239000;School of Mathematics and Finance,Chuzhou University,Chuzhou 239000)

机构地区：[1]滁州学院计算机与信息工程学院,滁州239000 [2]滁州学院数学与金融学院,滁州239000

出　　处：《工程数学学报》2022年第4期672-680,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(12147115);中国博士后科学基金(2022M712833);安徽省自然科学基金(2108085QA09);安徽省高校自然科学研究项目(KJ2021A1094,KJ2021B03)。

摘　　要：从矩阵谱问题出发,讨论了一类广义NLS-MKdV方程族和双哈密顿结构。首先,基于Loop Lie代数sl (2, R)构造了的广义NLS-MKdV方程族。其次,利用迹恒等式(变分恒等式)得到了广义NLS-MKdV方程的双Hamilton结构表示形式。再者,构造了带自相容源的广义NLS-MKdV方程族。最后,借助Riccati方程研究了广义NLSMKdV方程族的守恒律。Starting from the matrix spectral problem, a class of generalized NLS-MKdV hierarchy and bi-Hamiltonian structures are discussed. Firstly, a generalized NLS-MKdV hierarchy is constructed based on the Loop Lie algebra sl(2, R). Secondly, the bi-Hamilton structure representation of the generalized NLS-MKdV hierarchy is obtained by using the trace identity or variational identity. Furthermore, a class of generalized NLS-MKdV hierarchy with selfconsistent sources is constructed. Finally, the conservation laws of the generalized NLS-MKdV hierarchy are studied by means of the Riccati equation.

关 键 词：LIE代数 广义NLS-MKdV方程族 哈密顿结构 自相容源 守恒律 

分 类 号：O175.29[理学—数学]