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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 860935, 7 pages
http://dx.doi.org/10.1155/2014/860935
Research Article

Two Expanding Integrable Models of the Geng-Cao Hierarchy

1Department of Basic Courses, Shandong University of Science and Technology, Tai’an, Shandong 271019, China
2College of Science, China University of Mining and Technology, Xuzhou 221116, China

Received 21 November 2013; Accepted 13 January 2014; Published 27 February 2014

Academic Editor: Tiecheng Xia

Copyright © 2014 Xiurong Guo 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

As far as linear integrable couplings are concerned, one has obtained some rich and interesting results. In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC) hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually, it is a nonlinear integrable coupling) reduces to a generalized Burgers equation and further reduces to the heat equation whose expanding nonlinear integrable model is generated. Another one is an expanding integrable model which is different from the first one. Finally, the Hamiltonian structures of the two expanding integrable models are obtained by employing the variational identity and the trace identity, respectively.