Two types of loop algebras and their expanding Lax integrable models |
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Authors: | Yue Chao Zhang Yu-Feng and Wei Yuan |
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Institution: | School of Information Engineering, Taishan Medical University, Taian 271016, China; School of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China |
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Abstract: | Though various integrable
hierarchies of evolution equations were obtained by choosing
proper U in zero-curvature equation Ut-Vx+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 A2. 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. |
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Keywords: | zero-curvature equation integrable hierarchy loop algebra |
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