The multicomponent (2+1)-dimensional Glachette--Johnson (GJ) equation hierarchy and its super-integrable coupling system
Yu Fa-Jun(于发军)a)b)† and Zhang Hong-Qing(张鸿庆)b)
aSchool of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China; b Department of Mathematics, Dalian University of Technology, Dalian 116024, China
Abstract This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra $\tilde{A}_M$. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent (2+1)-dimensional Glachette--Johnson (GJ) hierarchy is given. Finally, the super-integrable coupling system of multicomponent (2+1)-dimensional GJ hierarchy is established through enlarging the spectral problem.
Received: 23 July 2007
Revised: 25 August 2007
Accepted manuscript online:
Fund: Project supported by the National
Key Basic Research Development of
China (Grant No 2004CB318000).
Cite this article:
Yu Fa-Jun(于发军) and Zhang Hong-Qing(张鸿庆) The multicomponent (2+1)-dimensional Glachette--Johnson (GJ) equation hierarchy and its super-integrable coupling system 2008 Chin. Phys. B 17 1574
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