Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 310945, 7 pages
http://dx.doi.org/10.1155/2015/310945
Research Article

Exact Periodic Wave, Bisoliton, and Various Breather Solutions for the Zakharov Equations

1College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
2City and Environment College, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China

Received 17 July 2015; Revised 2 November 2015; Accepted 5 November 2015

Academic Editor: Masoud Hajarian

Copyright © 2015 Heng Wang 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. Y. Shang and X. Zheng, “The first-integral method and abundant explicit exact solutions to the Zakharov equations,” Journal of Applied Mathematics, vol. 2012, Article ID 818345, 16 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  2. Y. Shang, Y. Huang, and W. Yuan, “The extended hyperbolic functions method and new exact solutions to the Zakharov equations,” Applied Mathematics and Computation, vol. 200, no. 1, pp. 110–122, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. D. J. Huang and H. Q. Zhang, “Extended hyperbolic function method and new exact solitary wave solutions of Zakharov equations,” Acta Physica Sinica, vol. 53, no. 8, pp. 2434–2438, 2004. View at Google Scholar · View at MathSciNet
  4. S. D. Liu, Z. T. Fu, S. K. Liu, and Q. Zhao, “Enveloping periodic solutions to nonlinear wave equations with Jacobi elliptic functions,” Acta Physica Sinica, vol. 51, no. 4, pp. 718–722, 2002. View at Google Scholar · View at MathSciNet
  5. G. Wu, M. Zhang, L. Shi, W. Zhang, and J. Han, “An extended expansion method or Jacobi elliptic functions and new exact periodic solutions of Zakharov equations,” Acta Physica Sinica, vol. 56, no. 9, pp. 5054–5059, 2007. View at Google Scholar
  6. C. H. Zhao and Z. M. Sheng, “Explicit travelling wave solutions for Zakharov equations,” Acta Physica Sinica, vol. 53, no. 6, pp. 1629–1634, 2004. View at Google Scholar · View at MathSciNet
  7. H. L. Zhen, B. Tian, Y. F. Wang et al., “Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma,” Physics of Plasmas, vol. 22, no. 3, Article ID 032307, 2015. View at Google Scholar
  8. X. Y. Gao, “Variety of the cosmic plasmas: general variable-coefficient Korteweg-de Vries-Burgers equation with experimental/observational support,” EPL, vol. 110, no. 1, Article ID 15002, p. 15002, 2015. View at Publisher · View at Google Scholar
  9. X. Y. Gao, “Comment on ‘Solitons, Bäcklund transformation, and Lax pair for the (2 + 1)-dimensional Boiti-Leon- Pempinelli equation for the water waves’ [J. Math. Phys. 51, 093519 (2010)],” Journal of Mathematical Physics, vol. 56, no. 1, Article ID 014101, 2015. View at Publisher · View at Google Scholar
  10. X.-Y. Gao, “Bäcklund transformation and shock-wave-type solutions for a generalized (3 + 1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid mechanics,” Ocean Engineering, vol. 96, pp. 245–247, 2015. View at Publisher · View at Google Scholar · View at Scopus
  11. X. Y. Gao, “Incompressible-fluid symbolic computation and Bäcklund transformation: (3 + 1)-dimensional variable-coefficient Boiti-Leon-Manna-Pempinelli model,” Zeitschrift für Naturforschung A, vol. 70, pp. 59–61, 2015. View at Google Scholar
  12. Y.-F. Wang, B. Tian, M. Wang, and H.-L. Zhen, “Solitons via an auxiliary function for an inhomogeneous higher-order nonlinear Schrödinger equation in optical fiber communications,” Nonlinear Dynamics, vol. 79, no. 1, pp. 721–729, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. W.-R. Sun, B. Tian, Y. Jiang, and H.-L. Zhen, “Optical rogue waves associated with the negative coherent coupling in an isotropic medium,” Physical Review E, vol. 91, no. 2, Article ID 023205, 2015. View at Publisher · View at Google Scholar · View at Scopus
  14. H.-F. Zhang, H.-Q. Hao, and J.-W. Zhang, “Breathers and soliton solutions for a generalization of the nonlinear Schrödinger equation,” Mathematical Problems in Engineering, vol. 2013, Article ID 456864, 5 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. C. Wang, Z. Dai, and C. Liu, “The breather-like and rational solutions for the integrable kadomtsev-petviashvili-based system,” Advances in Mathematical Physics, vol. 2015, Article ID 861069, 7 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  16. F. Fedele, “Rogue waves in oceanic turbulence,” Physica D: Nonlinear Phenomena, vol. 237, no. 14–17, pp. 2127–2131, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, “Rogue waves in mode-locked fiber lasers,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 85, Article ID 013828, 6 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. C. Bonatto, M. Feyereisen, S. Barland et al., “Deterministic optical rogue waves,” Physical Review Letters, vol. 107, no. 5, Article ID 053901, 5 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Physics Letters A, vol. 373, no. 6, pp. 675–678, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, “Extreme waves that appear from nowhere: on the nature of rogue waves,” Physics Letters A, vol. 373, no. 25, pp. 2137–2145, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus