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Abstract and Applied Analysis
Volume 2014, Article ID 146537, 7 pages
http://dx.doi.org/10.1155/2014/146537
Research Article

A Complex Integrable Hierarchy and Its Hamiltonian Structure for Integrable Couplings of WKI Soliton Hierarchy

College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034, China

Received 14 April 2014; Accepted 4 June 2014; Published 26 June 2014

Academic Editor: Huanhe Dong

Copyright © 2014 Fajun Yu et al. 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.

Abstract

We generate complex integrable couplings from zero curvature equations associated with matrix spectral problems in this paper. A direct application to the WKI spectral problem leads to a novel soliton equation hierarchy of integrable coupling system; then we consider the Hamiltonian structure of the integrable coupling system. We select the , and generate the nonlinear composite parts, which generate new extended WKI integrable couplings. It is also indicated that the method of block matrix is an efficient and straightforward way to construct the integrable coupling system.