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.
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 offer 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.
出处
《数学杂志》
CSCD
北大核心
2015年第3期539-548,共10页
Journal of Mathematics
基金
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)
关键词
零曲律方程
可积耦合
哈密顿结构
守恒律
zero curvature equations
integrable couplings
Hamiltonian structure
conservation laws
