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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 348796, 7 pages
http://dx.doi.org/10.1155/2014/348796
Research Article

Soliton and Breather Solutions for the Mixed Nonlinear Schrödinger Equation via -Fold Darboux Transformation

School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received 19 February 2014; Accepted 29 April 2014; Published 21 May 2014

Academic Editor: Abdul Hamid Kara

Copyright © 2014 Hui-Qin Hao 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. A. Biswas and S. Konar, “Quasi-particle theory of optical soliton interaction,” Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 7, pp. 1202–1228, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. R. Kohl, A. Biswas, D. Milovic, and E. Zerrad, “Optical soliton perturbation in a non-Kerr law media,” Optics and Laser Technology, vol. 40, no. 4, pp. 647–662, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. P. Green, D. Milovic, A. K. Sarma, D. A. Lott, and A. Biswas, “Dynamics of super-sech solitons in optical fibers,” Journal of Nonlinear Optical Physics and Materials, vol. 19, no. 2, pp. 339–370, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. L. Girgis, D. Milovic, S. Konar, A. Yildirim, H. Jafari, and A. Biswas, “Optical Gaussons in birefringent fibers and DWDM systems with intermodal dispersion,” Romanian Reports in Physics, vol. 64, no. 3, pp. 663–671, 2012. View at Google Scholar
  5. A. Biswas, M. Fessak, S. Johnson et al., “Optical soliton perturbation in non-Kerr law media: traveling wave solution,” Optics and Laser Technology, vol. 44, no. 1, pp. 263–268, 2012. View at Publisher · View at Google Scholar
  6. M. Savescu, K. R. Khan, R. W. Kohl, L. Moraru, A. Yildirim, and A. Biswas, “Optical soliton perturbation with improved nonlinear schrödinger's equation in nano fibers,” Journal of Nanoelectronics and Optoelectronics, vol. 8, no. 2, pp. 208–220, 2013. View at Google Scholar
  7. G. P. Agrawal, Nonlinear Fiber Optics, Academic Press, San Diego, Calif, USA, 2001.
  8. O. C. Wright, “Homoclinic connections of unstable plane waves of the modified nonlinear Schrödinger equation,” Chaos, Solitons and Fractals, vol. 20, no. 4, pp. 735–749, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. Z. Y. Chen and N. N. Huang, “Explicit N-soliton solution of the modified nonlinear Schrödinger equation,” Physical Review A, vol. 41, p. 4066, 1990. View at Publisher · View at Google Scholar
  10. S. L. Liu and W. Z. Wang, “Exact N-soliton solution of the modified nonlinear Schrödinger equation,” Physical Review E, vol. 48, p. 3054, 1993. View at Publisher · View at Google Scholar
  11. C. H. Gu, H. S. He, and Z. X. Zhou, Darboux Transformation in Soliton Theory and Its Geometric Applications, Shanghai Scientific and Technical, Shanghai, China, 2005.
  12. V. B. Matveev and M. A. Sall', “Scattering of solitons in the formalism of the Darboux transform,” Journal of Soviet Mathematics, vol. 34, no. 5, pp. 1983–1987, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. R. Guo and H.-Q. Hao, “Breathers and localized solitons for the Hirota-Maxwell-Bloch system on constant backgrounds in erbium doped fibers,” Annals of Physics, vol. 344, pp. 10–16, 2014. View at Publisher · View at Google Scholar
  14. R. Guo and H.-Q. Hao, “Breathers and multi-soliton solutions for the higher-order generalized nonlinear Schrödinger equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 9, pp. 2426–2435, 2013. View at Google Scholar
  15. B. K. Som, M. R. Gupta, and B. Dasgupta, “Reduction of the Boussinesq type of equation to modified Hirota equation,” Journal of the Physical Society of Japan, vol. 47, no. 4, pp. 1296–1298, 1979. View at Google Scholar · View at Scopus
  16. K. Tai, A. Tomita, and A. Hasegawa, “Observation of modulational instability in optical fibers,” Physical Review Letters, vol. 56, p. 135, 1986. View at Publisher · View at Google Scholar