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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 520765, 8 pages
http://dx.doi.org/10.1155/2013/520765
Research Article

Nonlinear Super Integrable Couplings of Super Broer-Kaup-Kupershmidt Hierarchy and Its Super Hamiltonian Structures

1School of Mathematics and Information Science, Shangqiu Normal University, Shangqiu 476000, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 25 February 2013; Revised 26 July 2013; Accepted 9 August 2013

Academic Editor: Xing Biao Hu

Copyright © 2013 Sixing Tao and Tiecheng Xia. 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

Nonlinear integrable couplings of super Broer-Kaup-Kupershmidt hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction, nonlinear integrable couplings of the classical integrable hierarchy were obtained.