Two types of loop algebras and their expanding Lax integrable models
Yue Chao(岳超)a)†, Zhang Yu-Feng(张玉峰)b)‡, and Wei Yuan(魏媛)b)
a School of Information Engineering, Taishan Medical University, Taian 271016, China; b School of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China
Abstract Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation $U _{t}-V_ {x}+[U,V]=0$, but in this paper, a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials. Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator $\widetilde{J}$ is presented by constructing a subalgebra $\widetilde{G}$ of the loop algebra $\widetilde{A}_{2}$. As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers, their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.
Received: 10 June 2005
Revised: 14 April 2006
Accepted manuscript online:
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