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Advances in Mathematical Physics
Volume 2015, Article ID 154915, 8 pages
http://dx.doi.org/10.1155/2015/154915
Research Article

Two Kinds of New Integrable Couplings of the Negative-Order Korteweg-de Vries Equation

1School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China
2College of Sciences, China University of Mining and Technology, Xuzhou 221116, China

Received 28 October 2014; Revised 25 November 2014; Accepted 17 December 2014

Academic Editor: Stephen C. Anco

Copyright © 2015 Binlu Feng and Yufeng Zhang. 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

Based on some known loop algebras with finite dimensions, two different negative-order integrable couplings of the negative-order Korteweg-de Vries (KdV) hierarchy of evolution equations are generated by making use of the Tu scheme, from which the corresponding negative-order integrable couplings of the negative-order KdV equations are followed to be obtained. The resulting Hamiltonian structure of one negative integrable coupling is derived from the variational identity.