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Solitary wave solutions for the KdV and mKdV equations by differential transform method

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  • Kangalgil, Figen
  • Ayaz, Fatma

Abstract

In this paper, we aim to present a reliable algorithm in order to obtain exact and approximate solutions for the nonlinear dispersive KdV and mKdV equations with initial profile. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. We first present the definition and operation of the two-dimensional differential transform and investigate the soliton solutions of Kdv and mKdV equations are obtained by the present method. Therefore, in the present work, numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.

Suggested Citation

  • Kangalgil, Figen & Ayaz, Fatma, 2009. "Solitary wave solutions for the KdV and mKdV equations by differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 464-472.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:464-472
    DOI: 10.1016/j.chaos.2008.02.009
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    References listed on IDEAS

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    1. Abdel-Halim Hassan, I.H., 2008. "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 53-65.
    2. Zhu, Yonggui & Chang, Qianshun & Wu, Shengchang, 2005. "Exact solitary-wave solutions with compact support for the modified KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 365-369.
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    Cited by:

    1. Hassan Eltayeb, 2013. "Note on Relation between Double Laplace Transform and Double Differential Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. H. M. Abdelhafez, 2016. "Solution of Excited Non-Linear Oscillators under Damping Effects Using the Modified Differential Transform Method," Mathematics, MDPI, vol. 4(1), pages 1-12, March.
    3. Mehmet Merdan & Ahmet Gökdoğan & Ahmet Yıldırım & Syed Tauseef Mohyud-Din, 2012. "Numerical Simulation of Fractional Fornberg‐Whitham Equation by Differential Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Younghae Do & Bongsoo Jang, 2012. "Enhanced Multistage Differential Transform Method: Application to the Population Models," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Brahim Benhammouda & Hector Vazquez-Leal & Arturo Sarmiento-Reyes, 2014. "Modified Reduced Differential Transform Method for Partial Differential‐Algebraic Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    6. Younghae Do & Bongsoo Jang, 2012. "Nonlinear Klein‐Gordon and Schrödinger Equations by the Projected Differential Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Ravi Kanth, A.S.V. & Aruna, K., 2009. "Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2277-2281.

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