Table of Contents
ISRN Computational Mathematics
Volume 2012 (2012), Article ID 423469, 5 pages
http://dx.doi.org/10.5402/2012/423469
Research Article

Laplace Decomposition Method to Study Solitary Wave Solutions of Coupled Nonlinear Partial Differential Equation

1Department of Mathematics, Government College, Kota, India
2Department of Mathematics, J.N.V. University, Jodhpur, India

Received 2 May 2012; Accepted 13 June 2012

Academic Editors: P. Amodio and L. S. Heath

Copyright © 2012 Arun Kumar and Ram Dayal Pankaj. 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. L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhäauser, Boston, Mass, USA, 1997.
  2. J. D. Logan, An Introduction to Nonlinear Partial Differential Equations, Wiley-Inter Science, New York, NY, USA, 1994.
  3. G. B. Whitham, Linear and Nonlinear Waves, Wiley, New York, NY, USA, 1974.
  4. C. Lubich and A. Ostermann, “Multi-grid dynamic iteration for parabolic equations,” BIT Numerical Mathematics, vol. 27, no. 2, pp. 216–234, 1987. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Vandewalle and R. Piessens, “Numerical experiments with nonlinear multigrid waveform relaxation on a parallel processor,” Applied Numerical Mathematics, vol. 8, no. 2, pp. 149–161, 1991. View at Google Scholar · View at Scopus
  6. G. Adomian, “The diffusion-Brusselator equation,” Computers and Mathematics with Applications, vol. 29, no. 5, pp. 1–3, 1995. View at Google Scholar · View at Scopus
  7. S. A. Khuri, “A Laplace decomposition algorithm applied to a class of nonlinear differential equations,” Journal of Applied Mathematics, vol. 1, no. 4, pp. 141–155, 2001. View at Publisher · View at Google Scholar · View at Scopus
  8. S. A. Khuri, “A new approach to Bratu's problem,” Applied Mathematics and Computation, vol. 147, no. 1, pp. 131–136, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. E. Yusufoglu, “Numerical solution of Duffing equation by the Laplace decomposition algorithm,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 572–580, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. N. S. Elgazery, “Numerical solution for the Falkner-Skan equation,” Chaos, Solitons and Fractals, vol. 35, no. 4, pp. 738–746, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Hussain and M. Khan, “Modified Laplace decomposition method,” Applied Mathematical Sciences, vol. 4, no. 33-35, pp. 1769–1783, 2010. View at Google Scholar · View at Scopus
  12. A. M. Wazwaz, Partial Differential Equations Methods and Applications, Balkema, Rotterdam, The Netherlands, 2002.
  13. A. M. Wazwaz, “The variational iteration method for solving linear and nonlinear systems of PDEs,” Computers and Mathematics with Applications, vol. 54, no. 7-8, pp. 895–902, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Kumar, “A variational description of non-linear Schrödinger Equation,” International Journal of Computational and Applied Mathematics, vol. 4, no. 2, pp. 159–164, 2009. View at Google Scholar
  15. V. E. Zakharov, “Collapse of Langmuir waves,” Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki, vol. 62, pp. 1745–1751, 1972. View at Google Scholar
  16. A. M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, The Netherlands, 2002.