Skip to main content
SpringerLink
Log in

Numerical analysis of higher-dimensional dispersive long-wave equations

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In this paper, numerical analysis of the (2+1)-dimensional dispersive long-wave equation (DLWE) is studied by using the homotopy perturbation method (HPM). For this purpose, the available analytical solutions obtained by multiple traveling-wave solution will be compared to show the validity and accuracy of the presented numerical algorithm. The obtained results prove the convergence and accuracy of the HPM for the numerically analyzed (2+1)-dimensional DLWE system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Wang M.L.: Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213, 279–287 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Boiti M., Leon J., Pempinelli F.: Spectral tranform for a two spatial dimension extension of the dispersive long wave equation. Inverse Probl. 13, 371–387 (1987)

    Article  MathSciNet  Google Scholar 

  3. Fan E.: Multiple traveling wave solutions of nonlinear evolution equations using a unified algebraic method. J. Phys. A Math. Gen. 35, 6853–6872 (2002)

    Article  MATH  Google Scholar 

  4. Eckhaus W.: Similarity Solutions Of Dispersive Long Wave Equations in Two Space Dimensions. Lecture Notes in Physics, vol. 249. Springer, Berlin (1986)

    Google Scholar 

  5. Paquin G., Winternitz P.: Group theoretical-analysis of dispersive long-wave equations in 2 space dimensions. Phys. D 46(1), 122–138 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lou S.Y.: Similarity solutions of dispersive long-wave equations in 2 space dimensions. Math. Meth. Appl. Sci. 18(10), 789–802 (1995)

    Article  MATH  Google Scholar 

  7. Tang X.Y., Lou S.Y.: Folded solitary waves and foldons in (2+1) dimensions. Commun. Theor. Phys. 40(1), 62–66 (2003)

    MathSciNet  Google Scholar 

  8. He J.H.: An approximate solution technique depending on an artificial parameter: a special example. Commun. Nonlin. Sci. Numer. Simul. 3(2), 92–97 (1998)

    Article  MATH  Google Scholar 

  9. He J.H.: Homotopy perturbation technique. Comput. Meth. Appl. Mech. Eng. 178(3–4), 257–262 (1999)

    Article  MATH  Google Scholar 

  10. He J.H.: A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int. J. Nonlin. Mech. 35(1), 37–43 (2000)

    Article  MATH  Google Scholar 

  11. He J.H.: Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput. 135, 73–79 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. He J.H.: Comparison of homotopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156, 527–539 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gorji M., Ganji D.D., Soleimani S.: New application of He’s homotopy perturbation method. Int. J. Nonlin. Sci. 8(3), 319–328 (2007)

    Google Scholar 

  14. Biazar J., Eslami M., Ghazvini H.: Homotopy perturbation method for systems of partial differential equations. Int. J. Nonlin. Sci. 8(3), 413–418 (2007)

    Google Scholar 

  15. Öziş T., Yıldırım A.: Traveling wave solution of Korteweg-de Vries equation using He’s homotopy perturbation method. Int. J. Nonlin. Sci. 8(2), 239–242 (2007)

    Google Scholar 

  16. Ganji D.D., Sadighi A.: Application of He’s homotopy-perturbation method to nonlinear coupled systems of reaction–diffusion equations. Int. J. Nonlin. Sci. 7(4), 411–418 (2006)

    Google Scholar 

  17. Rafei M., Ganji D.D.: Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method. Int. J. Nonlin. Sci. 7(3), 321–328 (2006)

    Google Scholar 

  18. He J.H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20(10), 1141–1199 (2006)

    Article  MATH  Google Scholar 

  19. He J.H.: New interpretation of homotopy perturbation method. Int. J. Mod. Phys. B 20(18), 2561–256 (2006)

    Article  Google Scholar 

  20. Abbasbandy S.: The application of homotopy analysis method to solve a generalized Hirota Satsuma coupled KdV equation. Phys. Lett. A 361, 478–483 (2007)

    Article  MATH  Google Scholar 

  21. Refai M., Ganji D.D., Daniali H.R.M., Pashaei H.: Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations. Phys. Lett. A 364, 1–6 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Sciences, Istanbul Technical University, Istanbul, Turkey

    Semih Küçükarslan

Authors
  1. Semih Küçükarslan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Semih Küçükarslan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Küçükarslan, S. Numerical analysis of higher-dimensional dispersive long-wave equations. Arch Appl Mech 79, 433–440 (2009). https://doi.org/10.1007/s00419-008-0241-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-008-0241-6

Keywords

Search

Navigation