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Abstract and Applied Analysis
Volume 2014, Article ID 235159, 6 pages
http://dx.doi.org/10.1155/2014/235159
Research Article

Conservation Laws and Self-Consistent Sources for an Integrable Lattice Hierarchy Associated with a Three-by-Three Discrete Matrix Spectral Problem

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2Institute of Oceanology, China Academy of Sciences, Qingdao 266071, China
3Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China

Received 25 June 2014; Accepted 14 August 2014; Published 19 October 2014

Academic Editor: Huanhe Dong

Copyright © 2014 Yu-Qing Li and Bao-Shu Yin. 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

A lattice hierarchy with self-consistent sources is deduced starting from a three-by-three discrete matrix spectral problem. The Hamiltonian structures are constructed for the resulting hierarchy. Liouville integrability of the resulting equations is demonstrated. Moreover, infinitely many conservation laws of the resulting hierarchy are obtained.