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Advances in Mathematical Physics
Volume 2016, Article ID 3589704, 6 pages
Research Article

A Soliton Hierarchy Associated with a Spectral Problem of 2nd Degree in a Spectral Parameter and Its Bi-Hamiltonian Structure

1Department of Applied Mathematics, China Agricultural University, Beijing 100083, China
2Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA
3Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China

Received 22 January 2016; Accepted 15 March 2016

Academic Editor: Boris G. Konopelchenko

Copyright © 2016 Yuqin Yao 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.


Associated with , a new matrix spectral problem of 2nd degree in a spectral parameter is proposed and its corresponding soliton hierarchy is generated within the zero curvature formulation. Bi-Hamiltonian structures of the presented soliton hierarchy are furnished by using the trace identity, and thus, all presented equations possess infinitely commuting many symmetries and conservation laws, which implies their Liouville integrability.