A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures

doi:10.1088/1674-1056/23/6/060201

中国物理B ›› 2014, Vol. 23 ›› Issue (6): 60201-060201.doi: 10.1088/1674-1056/23/6/060201

A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures

翟云云^a, 耿献国^a, 何国亮^b

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

收稿日期:2013-11-11 修回日期:2013-12-10 出版日期:2014-06-15 发布日期:2014-06-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11331008 and 11171312).

A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures

Zhai Yun-Yun (翟云云)^a, Geng Xian-Guo (耿献国)^a, He Guo-Liang (何国亮)^b

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

Received:2013-11-11 Revised:2013-12-10 Online:2014-06-15 Published:2014-06-15
Contact: Zhai Yun-Yun E-mail:zhai1226@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11331008 and 11171312).

摘要/Abstract

摘要： 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.

关键词: spectral problem, nonlinear evolution equations, bi-Hamiltonian structure, conservation laws

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.

Key words: spectral problem, nonlinear evolution equations, bi-Hamiltonian structure, conservation laws

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems)

翟云云, 耿献国, 何国亮. A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures[J]. 中国物理B, 2014, 23(6): 60201-060201.

Zhai Yun-Yun (翟云云), Geng Xian-Guo (耿献国), He Guo-Liang (何国亮). A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures[J]. Chin. Phys. B, 2014, 23(6): 60201-060201.

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A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures

A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures

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