About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 158140, 5 pages
http://dx.doi.org/10.1155/2013/158140
Research Article

Various Heteroclinic Solutions for the Coupled Schrödinger-Boussinesq Equation

1School of Information Science and Engineering, Yunnan University, Kunming 650091, China
2School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

Received 31 December 2012; Accepted 21 February 2013

Academic Editor: Peicheng Zhu

Copyright © 2013 Murong Jiang and Zhengde Dai. 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. M. J. Ablowitz and B. M. Herbst, “On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation,” SIAM Journal on Applied Mathematics, vol. 50, no. 2, pp. 339–345, 1990. View at Zentralblatt MATH · View at MathSciNet
  2. N. Ercolani, M. G. Forest, and D. W. McLaughlin, “Geometry of the modulational instability. III. Homoclinic orbits for the periodic sine-Gordon equation,” Physica D, vol. 43, no. 2-3, pp. 349–384, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Z. Dai and J. Huang, “Homoclinic tubes for the Davey-Stewartson II equation with periodic boundary conditions,” Chinese Journal of Physics, vol. 43, no. 2, pp. 349–360, 2005. View at MathSciNet
  4. Z. Dai, J. Huang, M. Jiang, and S. Wang, “Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint,” Chaos, Solitons and Fractals, vol. 26, no. 4, pp. 1189–1194, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Z. Dai, J. Huang, and M. Jiang, “Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary,” Physics Letters A, vol. 352, no. 4-5, pp. 411–415, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. N. N. Rao, “Near-magnetosonic envelope upper-hybrid waves,” Journal of Plasma Physics, vol. 39, no. 3, pp. 385–392, 1988. View at Scopus
  7. Y. Hase and J. Satsuma, “An N-soliton solution for the nonlinear Schrödinger equation coupled to the Boussinesq equation,” Journal of the Physical Society of Japan, vol. 57, no. 3, pp. 679–682, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  8. R. Conte and M. Mussete, “Link between solitary waves and Riccati equation,” Journal of Physics A, vol. 25, pp. 5600–5615, 1992.
  9. A. R. Chowdhury, B. Dasgupta, and N. N. Rao, “Painléve analysis and Backlund transformations for coupled generalized Schrödinger-Boussinesq system,” Chaos, Solitons and Fractals, vol. 9, no. 10, pp. 1747–1753, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  10. X. B. Hu, B. L. Guo, and H. W. Tam, “Homoclinic orbits for the coupled Schrödinger-Boussinesq equation and coupled higgs equation,” Journal of the Physical Society of Japan, vol. 72, no. 1, pp. 189–190, 2003. View at Publisher · View at Google Scholar · View at Scopus
  11. Z. D. Dai, Z. J. Liu, and D. L. Li, “Exact periodic solitary-wave solution for KdV equation,” Chinese Physics Letters, vol. 25, no. 5, pp. 1531–1534, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. Dai, J. Liu, and D. Li, “Applications of HTA and EHTA to YTSF equation,” Applied Mathematics and Computation, vol. 207, no. 2, pp. 360–364, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. Dai, Z. Li, Z. Liu, and D. Li, “Exact homoclinic wave and soliton solutions for the 2D Ginzburg-Landau equation,” Physics Letters A, vol. 372, no. 17, pp. 3010–3014, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. G. Mu and Z. Qin, “Rogue waves for the coupled Schrödinger-Boussinesq equation and the coupled Higgs equation,” Journal of the Physical Society of Japan, vol. 81, Article ID 084001, 2012.