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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 6347961, 13 pages
Research Article

The Bi-Integrable Couplings of Two-Component Casimir-Qiao-Liu Type Hierarchy and Their Hamiltonian Structures

Department of Applied Mathematics, China Agricultural University, Beijing 100083, China

Received 13 March 2016; Accepted 29 June 2016

Academic Editor: Boris G. Konopelchenko

Copyright © 2016 Juhui Zhang and Yuqin Yao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new type of two-component Casimir-Qiao-Liu type hierarchy (2-CQLTH) is produced from a new spectral problem and their bi-Hamiltonian structures are constructed. Particularly, a new completely integrable two-component Casimir-Qiao-Liu type equation (2-CQLTE) is presented. Furthermore, based on the semidirect sums of matrix Lie algebras consisting of block matrix Lie algebra, the bi-integrable couplings of the 2-CQLTH are constructed and their bi-Hamiltonian structures are furnished.