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The Scientific World Journal
Volume 2014, Article ID 438345, 5 pages
http://dx.doi.org/10.1155/2014/438345
Research Article

An Analytical Study for (2 + 1)-Dimensional Schrödinger Equation

Department of Basic Sciences, Kermanshah University of Technology, Kermanshah, Iran

Received 30 August 2013; Accepted 30 October 2013; Published 27 January 2014

Academic Editors: N. Damil and X.-w. Gao

Copyright © 2014 Behzad Ghanbari. 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. Arnold, “Numerically absorbing boundary conditions for quantum evolution equations,” VLSI Design, vol. 6, no. 1–4, pp. 313–319, 1998. View at Google Scholar · View at Scopus
  2. S. A. Khuri, “A new approach to the cubic Schrodinger equation: an application of the decomposition technique,” Applied Mathematics and Computation, vol. 97, pp. 251–254, 1998. View at Google Scholar
  3. J. Biazar and H. Ghazvini, “Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method,” Physics Letters A, vol. 366, no. 1-2, pp. 79–84, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Biazar and B. Ghanbari, “The homotopy perturbation method for solving neutral functional-differential equations with proportional delays,” Journal of King Saud University-Science, vol. 24, no. 1, pp. 33–37, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. A. K. Alomari, M. S. M. Noorani, and R. Nazar, “Explicit series solutions of some linear and nonlinear Schrodinger equations via the homotopy analysis method,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1196–1207, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Mohebbi and M. Dehghan, “The use of compact boundary value method for the solution of two-dimensional Schrödinger equation,” Journal of Computational and Applied Mathematics, vol. 225, no. 1, pp. 124–134, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. N. H. Sweilam and R. F. Al-Bar, “Variational iteration method for coupled nonlinear Schrödinger equations,” Computers and Mathematics with Applications, vol. 54, no. 7-8, pp. 993–999, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. S. J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems [Ph.D. thesis], Shanghai Jiao Tong University, 1992.
  9. S. J. Liao, “On the homotopy analysis method for nonlinear problems,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 499–513, 2004. View at Publisher · View at Google Scholar · View at Scopus
  10. S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall, CRC Press, Boca Raton, Fla, USA, 2003.
  11. S. J. Liao, “Notes on the homotopy analysis method: some definitions and theorems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 983–997, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. S. J. Liao, “A new branch of solutions of boundary-layer flows over an impermeable stretched plate,” International Journal of Heat and Mass Transfer, vol. 48, no. 12, pp. 2529–2539, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. B. Ghanbari, L. Rada, and K. Chen, “A restarted iterative homotopy analysis method for twononlinear models from image processing,” International Journal of Computer Mathematics, 2013. View at Publisher · View at Google Scholar
  14. J. Biazar and B. Ghanbari, “HAM solution of some initial value problems arising in heat radiation equations,” Journal of King Saud University-Science, vol. 24, no. 2, pp. 161–165, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Liang and D. J. Jeffrey, “Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 12, pp. 4057–4064, 2009. View at Publisher · View at Google Scholar · View at Scopus