Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 932672, 9 pages
http://dx.doi.org/10.1155/2014/932672
Research Article

A Few Integrable Couplings of Some Integrable Systems and ()-Dimensional Integrable Hierarchies

1School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China
2College of Sciences, China University of Mining and Technology, Xuzhou 221116, China
3School of Mathematics, Shandong University of Science and Technology, Qingdao 266590, China

Received 25 April 2014; Accepted 20 July 2014; Published 14 August 2014

Academic Editor: Wen-Xiu Ma

Copyright © 2014 Binlu Feng 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.

Linked References

  1. F. Magri, “A simple model of the integrable Hamiltonian equation,” Journal of Mathematical Physics, vol. 19, no. 5, pp. 1156–1162, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. G. Z. Tu, “The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems,” Journal of Mathematical Physics, vol. 30, no. 2, pp. 330–338, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. W. X. Ma, “A hierarchy of Liouville integrable generalized Hamiltonian equations and its reduction,” Chinese Journal of Contemporary Mathematics, vol. 13, no. 1, pp. 79–89, 1992. View at Google Scholar · View at MathSciNet
  4. W. X. Ma, “A hierarchy of Liouville integrable finite-dimensional Hamiltonian systems,” Applied Mathematics and Mechanics, vol. 13, no. 4, pp. 369–377, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. W. Ma, “An approach for constructing non-isospectral hierarchies of evolution equations,” Journal of Physics A: Mathematical and General, vol. 25, no. 12, pp. L719–L726, 1992. View at Publisher · View at Google Scholar · View at Scopus
  6. W. Ma, “A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order,” Physics Letters. A, vol. 367, no. 6, pp. 473–477, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. X. B. Hu, “A powerful approach to generate new integrable systems,” Journal of Physics A: Mathematical and General, vol. 27, no. 7, pp. 2497–2514, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. X. Hu, “An approach to generate superextensions of integrable systems,” Journal of Physics A: Mathematical and General, vol. 30, no. 2, pp. 619–632, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. E. Fan, “A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations,” Journal of Mathematical Physics, vol. 42, no. 9, pp. 4327–4344, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. E. G. Fan, “Integrable evolution systems based on Gerdjikov-Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation,” Journal of Mathematical Physics, vol. 41, no. 11, pp. 7769–7782, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. S. Chakravarty, S. L. Kent, and E. T. Newman, “Some reductions of the self-dual Yang-Mills equations to integrable systems in 2+1 dimensions,” Journal of Mathematical Physics, vol. 36, no. 2, pp. 763–772, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. M. J. Ablowitz, S. Chakravarty, and L. A. Takhtajan, “A self-dual Yang-Mills hierarchy and its reductions to integrable systems in 1 + 1 and 2 + 1 dimensions,” Communications in Mathematical Physics, vol. 158, no. 2, pp. 289–314, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. G. Z. Tu, R. I. Andrushkiw, and X. C. Huang, “A trace identity and its application to integrable systems of 1+2 dimensions,” Journal of Mathematical Physics, vol. 32, no. 7, pp. 1900–1907, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. G. Z. Tu and D. Z. Meng, “The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems (II),” Acta Mathematicae Applicatae Sinica, vol. 5, no. 1, pp. 89–96, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. W. Ma and M. Chen, “Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras,” Journal of Physics A: Mathematical and General, vol. 39, no. 34, pp. 10787–10801, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus