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Solitary wave solutions to the Kuramoto–Sivashinsky equation by means of the homotopy analysis method

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Abstract

The homotopy analysis method (HAM) is used to find a family of solitary solutions of the Kuramoto–Sivashinsky equation. This approximate solution, which is obtained as a series of exponentials, has a reasonable residual error. The homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of series solution. This method is reliable and manageable.

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Authors and Affiliations

  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14778, Iran

    S. Abbasbandy

  2. Department of Mathematics, Imam Khomeini International University, Ghazvin, 34194, Iran

    S. Abbasbandy

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  1. S. Abbasbandy
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Correspondence to S. Abbasbandy.

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Abbasbandy, S. Solitary wave solutions to the Kuramoto–Sivashinsky equation by means of the homotopy analysis method. Nonlinear Dyn 52, 35–40 (2008). https://doi.org/10.1007/s11071-007-9255-9

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  • DOI: https://doi.org/10.1007/s11071-007-9255-9

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