Pure and Applied Mathematics Journal

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Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation

Received: 12 October 2015    Accepted: 21 October 2015    Published: 03 November 2015
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Abstract

In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.

DOI 10.11648/j.pamj.20150406.17
Published in Pure and Applied Mathematics Journal (Volume 4, Issue 6, December 2015)
Page(s) 264-268
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Laplace Transform, Homotopy Perturbation Method, Korteweg-DeVries (KDV) Equation

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Author Information
  • Department of Mathematic, Faculty of Sciences, Sudan University of Sciences and Technology, Khartoum, Sudan

  • Mathematics Department, Faculty of Sciences and Arts-Alkamil, University of Jeddah, Jeddah, Saudi Arabia

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  • APA Style

    Mohannad H. Eljaily, Tarig M. Elzaki. (2015). Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure and Applied Mathematics Journal, 4(6), 264-268. https://doi.org/10.11648/j.pamj.20150406.17

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    ACS Style

    Mohannad H. Eljaily; Tarig M. Elzaki. Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure Appl. Math. J. 2015, 4(6), 264-268. doi: 10.11648/j.pamj.20150406.17

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    AMA Style

    Mohannad H. Eljaily, Tarig M. Elzaki. Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation. Pure Appl Math J. 2015;4(6):264-268. doi: 10.11648/j.pamj.20150406.17

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  • @article{10.11648/j.pamj.20150406.17,
      author = {Mohannad H. Eljaily and Tarig M. Elzaki},
      title = {Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {6},
      pages = {264-268},
      doi = {10.11648/j.pamj.20150406.17},
      url = {https://doi.org/10.11648/j.pamj.20150406.17},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20150406.17},
      abstract = {In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.},
     year = {2015}
    }
    

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    T1  - Homotopy Perturbation Transform Method for Solving Korteweg-DeVries (KDV) Equation
    AU  - Mohannad H. Eljaily
    AU  - Tarig M. Elzaki
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    UR  - https://doi.org/10.11648/j.pamj.20150406.17
    AB  - In this paper, a combined form of the Laplace transforms method with the homotopy perturbation method is proposed to solve Korteweg-DeVries (KDV) Equation. This method is called the homotopy perturbation transform method (HPTM). The (HPTM) finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results reveal that the proposed method is very efficient, simple and can be applied to other nonlinear problems.
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