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| 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 |
| DOI： |
| 分类号:0175.29 |
| 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). |
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| CONSERVATION LAWS AND HAMILTONIANSTRUCTURE FOR A NONLINEAR INTEGRABLECOUPLINGS OF GUO SOLITON HIERARCHY |
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WEI Han-yu,XIA Tie-cheng
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| 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. |
| Key words: zero curvature equations integrable couplings Hamiltonian structure conservation laws |
