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Abstract and Applied Analysis
Volume 2018, Article ID 8325919, 8 pages
https://doi.org/10.1155/2018/8325919
Research Article

Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

Al-Rafidain University College, Baghdad, Iraq

Correspondence should be addressed to Anwar Ja’afar Mohamad Jawad; moc.oohay@1002dawaj_rawna

Received 8 September 2017; Accepted 26 October 2017; Published 1 January 2018

Academic Editor: Changbum Chun

Copyright © 2018 Anwar Ja’afar Mohamad Jawad and Mahmood Jawad Abu-AlShaeer. 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. 339–351, 1990. View at Publisher · View at Google Scholar · 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: Nonlinear Phenomena, vol. 43, no. 2-3, pp. 349–384, 1990. View at Publisher · View at Google Scholar · 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. 349–356, 2005. View at Google Scholar · View at MathSciNet · View at Scopus
  4. Z. Dai, J. Huang, M. Jiang, and S. Wang, “Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint,” Chaos, Solitons & Fractals, vol. 26, no. 4, pp. 1189–1194, 2005. View at Publisher · View at Google Scholar · View at Scopus
  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 MathSciNet · View at Scopus
  6. A. J. M. Jawad, “Soliton Solutions for Nonlinear Systems (2+1)-Dimensional Equations,” IOSR Journal of Mathematics, vol. 1, no. 6, pp. 27–34, 2012. View at Publisher · View at Google Scholar
  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. B. L. Guo and L. J. Shen, “The global solution of initial value problem for nonlinear Schrödinger-Boussinesq equation in 3-dimensions,” Acta Mathematicae Applicatae Sinica. English Series, vol. 6, no. 1, pp. 11–21, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  9. B. Guo and X. Du, “Existence of the periodic solution for the weakly damped Schrödinger–Boussinesq equation,” Journal of Mathematical Analysis and Applications, vol. 262, no. 2, pp. 453–472, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. A. Kilicman and R. Abazari, “Travelling wave solutions of the SchröDinger-Boussinesq system,” Abstract and Applied Analysis, vol. 2012, Article ID 198398, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Y. Lai and B. Wiwatanapataphe, “The asymptotics of global solutions for semilinear wave equations in two space dimensions,” Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms, vol. 18, no. 5, pp. 647–657, 2011. View at Google Scholar · View at MathSciNet
  12. S. Lai, Y. H. Wu, and B. Wiwatanapataphee, “On exact travelling wave solutions for two types of nonlinear k(n, n) equations and a generalized KP equation,” Journal of Computational and Applied Mathematics, vol. 212, no. 2, pp. 291–299, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  13. R. Conte and M. Musette, “Link between solitary waves and projective Riccati equations,” Journal of Physics A: Mathematical and General, vol. 25, no. 21, pp. 5609–5623, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. X. Huang, “The investigation of solutions to the coupled Schrödinger-Boussinesq equations,” Abstract and Applied Analysis, vol. 2013, Article ID 170372, 5 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. A. R. Chowdhury, B. Dasgupta, and N. N. Rao, “Painléve analysis and Backlund transformations for coupled generalized Schrödinger-Boussinesq system,” Chaos, Solitons & Fractals, vol. 9, no. 10, pp. 1747–1753, 1998. View at Publisher · View at Google Scholar · View at Scopus
  16. 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
  17. 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. 1531–1533, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. 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 MathSciNet · View at Scopus
  19. 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 MathSciNet · View at Scopus
  20. 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, no. 8, Article ID 084001, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. A. J. M. Jawad, M. Mirzazadeh, and A. Biswas, “Solitary wave solutions to nonlinear evolution equations in mathematical physics,” Pramana—Journal of Physics, vol. 83, no. 4, pp. 457–471, 2014. View at Publisher · View at Google Scholar · View at Scopus
  22. A. J. Jawad, “Three Different Methods for New Soliton Solutions of the Generalized NLS Equation,” Abstract and Applied Analysis, vol. 2017, Article ID 5137946, 8 pages, 2017. View at Publisher · View at Google Scholar
  23. A. J. Mohamad Jawad, M. D. Petkovi\'c, and A. Biswas, “Modified simple equation method for nonlinear evolution equations,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 869–877, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus