Nonlinear Integrable Couplings of Levi Hierarchy and WKI HierarchyReport as inadecuate




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Abstract and Applied Analysis - Volume 2014 2014, Article ID 678725, 7 pages -

Research Article

Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China

School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China

Graduate School, University of Chinese Academy of Sciences, Beijing 100049, China

Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received 11 June 2014; Accepted 2 July 2014; Published 14 July 2014

Academic Editor: Yufeng Zhang

Copyright © 2014 Zhengduo Shan 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

With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa WKI hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.





Author: Zhengduo Shan, Hongwei Yang, and Baoshu Yin

Source: https://www.hindawi.com/



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