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Chin. Phys. B, 2014, Vol. 23(6): 060201    DOI: 10.1088/1674-1056/23/6/060201
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A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures

Zhai Yun-Yuna, Geng Xian-Guoa, He Guo-Liangb
a School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
b School of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China
Abstract  With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3×3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy.
Keywords:  spectral problem      nonlinear evolution equations      bi-Hamiltonian structure      conservation laws     
Received:  11 November 2013      Published:  15 June 2014
PACS:  02.30.Jr (Partial differential equations)  
  02.30.Ik (Integrable systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11331008 and 11171312).
Corresponding Authors:  Zhai Yun-Yun     E-mail:

Cite this article: 

Zhai Yun-Yun, Geng Xian-Guo, He Guo-Liang A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures 2014 Chin. Phys. B 23 060201

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