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Guo族非线性可积耦合的哈密顿结构及其守恒
引用本文:魏含玉,夏铁成.Guo族非线性可积耦合的哈密顿结构及其守恒[J].数学杂志,2015,35(3):539-548.
作者姓名:魏含玉  夏铁成
作者单位:周口师范学院数学与统计学院, 河南 周口 466001;上海大学数学系, 上海 200444,上海大学数学系, 上海 200444
基金项目:Supported by National Natural Science Foundation of China(11271008; 61072147); the Shanghai Leading Academic Discipline Project(J50101); the Shanghai Univ. Leading Academic Discipline Project (A.13-0101-12-004); the Science and Technology Department of Henan Province(142300410253; 142300410324).
摘    要:基于可积耦合的基本理论,我们给出了构造孤子族非线性可积耦合的一般方法,并用相应圈代数上的变分恒等式来求可积耦合的哈密顿结构.作为应用,我们给出了Guo族的非线性可积耦合及其哈密顿结构.最后,给出了Guo族非线性可积耦合的守恒律.

关 键 词:零曲律方程  可积耦合  哈密顿结构  守恒律
收稿时间:2013/9/17 0:00:00
修稿时间:2014/4/21 0:00:00

CONSERVATION LAWS AND HAMILTONIANSTRUCTURE FOR A NONLINEAR INTEGRABLECOUPLINGS OF GUO SOLITON HIERARCHY
WEI Han-yu and XIA Tie-cheng.CONSERVATION LAWS AND HAMILTONIANSTRUCTURE FOR A NONLINEAR INTEGRABLECOUPLINGS OF GUO SOLITON HIERARCHY[J].Journal of Mathematics,2015,35(3):539-548.
Authors:WEI Han-yu and XIA Tie-cheng
Institution:College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;Department of Mathematics, Shanghai University, Shanghai 200444, China and Department of Mathematics, Shanghai University, Shanghai 200444, China
Abstract:In this paper, based on the rudimentary knowledge of the nonlinear integrable couplings, we establish a scheme for constructing nonlinear integrable Hamiltonian couplings of soliton hierarchy. Variational identities over the corresponding loop algebras are used to ofier Hamiltonian structures for the resulting integrable couplings. As an application, we use this method to obtain a nonlinear integrable couplings and Hamiltonian structure of the Guo hierarchy. Finally, we present the conservation laws for the nonlinear integrable couplings of the Guo soliton hierarchy.
Keywords:zero curvature equations  integrable couplings  Hamiltonian structure  conservation laws
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