An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system |
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| Authors: | Zhang Yu-Feng |
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| Affiliation: | Institute of Mathematics, Information School, Shandong University of Science and Technology, Taian 271019, China; Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | A subalgebra of loop algebra $\tilde{A}_2$ is established. Therefore, a new isospectral problem is designed. By making use of Tu's scheme, a new integrable system is obtained, which possesses bi-Hamiltonian structure. As its reductions, a formalism similar to the well-known Ablowitz－Kaup－Newell－Segur (AKNS) hierarchy and a generalized standard form of the Schr?dinger equation are presented. In addition, in order for a kind of expanding integrable system to be obtained, a proper algebraic transformation is supplied to change loop algebra $\tilde{A}_2$ into loop algebra $\tilde{A}_1$. Furthermore, a high-dimensional loop algebra is constructed, which is different from any previous one. An integrable coupling of the system obtained is given. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented. |
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| Keywords: | loop algebra integrable system Hamiltonian structure constrained flow |
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