About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 979252, 7 pages
http://dx.doi.org/10.1155/2013/979252
Research Article

Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term

Rui Cao1,2

1Department of Mathematics, Heze University, Heze 274000, China
2College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China

Received 12 July 2013; Accepted 10 September 2013

Academic Editor: Yong Hong Wu

Copyright © 2013 Rui Cao. 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. W.-X. Ma and M. Chen, “Direct search for exact solutions to the nonlinear Schrödinger equation,” Applied Mathematics and Computation, vol. 215, no. 8, pp. 2835–2842, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1981. View at MathSciNet
  3. A. Hasegawa and Y. Kodama, Solitons in Optical Communications, Oxford University Press, New York, NY, USA, 1995.
  4. L. X. Li and M. L. Wang, “The (G'/G)-expansion method and travelling wave solutions for a higher-order nonlinear Schrödinger equation,” Applied Mathematics and Computation, vol. 208, no. 2, pp. 440–445, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  5. W.-X. Ma and J.-H. Lee, “A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation,” Chaos, Solitons & Fractals, vol. 42, no. 3, pp. 1356–1363, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. X. Wu and Z. D. Dai, “New bright and dark solitons for quintic nonlinear derivative Schrödinger equation,” Applied Mathematics and Computation, vol. 218, no. 18, pp. 9305–9309, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. W. X. Ma, “Bilinear equations, Bell polynomials and linear superposition princ,” Journal of Physics, vol. 411, Article ID iple012021, 2013.
  8. Y. Liu, “Exact solutions to nonlinear Schrödinger equation with variable coefficients,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5866–5869, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. N. Taghizadeh and M. Mirzazadeh, “The simplest equation method to study perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1493–1499, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. N. A. Kudryashov, “On types of nonlinear nonintegrable equations with exact solutions,” Physics Letters A, vol. 155, no. 4-5, pp. 269–275, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  11. R. Hirota, The Direct Method in Soliton Theory, vol. 155, Cambridge University Press, Cambridge, UK, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  12. A. M. Wazwaz, “On multiple soliton solutions for coupled kdv-mkdv equation,” Nonlinear Science Letters A, vol. 1, no. 3, pp. 289–296, 2010.
  13. R. Hirota, “Direct method of finding exact solutions of nonlinear evolution equations,” in Bäcklund transformations, R. Bullough and P. Caudrey, Eds., Springer, Berlin, Germany, 1980. View at Zentralblatt MATH · View at MathSciNet
  14. A.-M. Wazwaz, “A sine-cosine method for handling nonlinear wave equations,” Mathematical and Computer Modelling, vol. 40, no. 5-6, pp. 499–508, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A.-M. Wazwaz, “The tanh method for traveling wave solutions of nonlinear equations,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 713–723, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. E. G. Fan, “Extended tanh-function method and its applications to nonlinear equations,” Physics Letters A, vol. 277, no. 4-5, pp. 212–218, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700–708, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. W.-X. Ma and Z. Zhu, “Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm,” Applied Mathematics and Computation, vol. 218, no. 24, pp. 11871–11879, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. E. G. Fan and J. Zhang, “Applications of the Jacobi elliptic function method to special-type nonlinear equations,” Physics Letters A, vol. 305, no. 6, pp. 383–392, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Z. S. Feng, “The first-integral method to study the Burgers-Korteweg-de Vries equation,” Journal of Physics A, vol. 35, no. 2, pp. 343–349, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. W.-X. Ma, “Comment on the 3+1 dimensional Kadomtsev-Petviashvili equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2663–2666, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. F. D. Xie, Y. Zhang, and Z. S. Lü, “Symbolic computation in non-linear evolution equation: application to (3+1)-dimensional Kadomtsev-Petviashvili equation,” Chaos, Solitons and Fractals, vol. 24, no. 1, pp. 257–263, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  23. C. P. Liu, “Exact solutions for the higher-order nonlinear Schördinger equation in nonlinear optical fibres,” Chaos, Solitons and Fractals, vol. 23, no. 3, pp. 949–955, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  24. S. Y. Lai, X. M. Lv, and M. Y. Shuai, “The Jacobi elliptic function solutions to a generalized Benjamin-Bona-Mahony equation,” Mathematical and Computer Modelling, vol. 49, no. 1-2, pp. 369–378, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet