A subalgebra of loop algebra $\tilde{A}_2$ and its applications
Zhang Yu-Feng (张玉峰)a, Tam Hon-Wah (谭汉华)b, Guo Fu-Kui (郭福奎)a
a Institute of Mathematics, Information School, Shandong University of Science and Technology, Taian 271019, China; b Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
Abstract A subalgebra of loop algebra $\tilde{A}_2$ and its expanding loop algebra $\overline{G}$ are constructed. It follows that both resulting integrable Hamiltonian hierarchies are obtained. As a reduction case of the first hierarchy, a generalized nonlinear coupled Schr?dinger equation, the standard heat-conduction and a formalism of the well known Ablowitz, Kaup, Newell and Segur hierarchy are given, respectively. As a reduction case of the second hierarchy, the nonlinear Schr?dinger and modified Korteweg de Vries hierarchy and a new integrable system are presented. Especially, a coupled generalized Burgers equation is generated.
Received: 30 May 2003
Revised: 28 August 2003
Accepted manuscript online:
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