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Semi-analytical Methods for Solving the KdV and mKdV Equations

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  • For another obtaining of the KdV equation for water waves, see Kevorkian and Cole (1981); one can see the work of the Johnson (1972) for a different water-wave application with variable depth, for waves on arbitrary shears in the work of Freeman and Johnson (1970) and Johnson (1980) for a review of one and two-dimensional KdV equations. In addition to these; one can see the book of Drazin and Johnson (1989) for some numerical solutions of nonlinear evolution equations. In the work of the Zabusky, Kruskal and Deam (F1965) and Eilbeck (F1981), one can see the motion pictures of soliton interactions. See a comparison of the KdV equation with water wave experiments in Hammack and Segur (1974)

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  1. Istanbul Commerce University, Faculty of Engineering, Istanbul, Turkey

    Doğan Kaya

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  1. Doğan Kaya
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    Robert A. Meyers

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Kaya, D. (2018). Semi-analytical Methods for Solving the KdV and mKdV Equations. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_305-3

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  • DOI: https://doi.org/10.1007/978-3-642-27737-5_305-3

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Chapter history

  1. Latest

    Semi-analytical Methods for Solving the KdV and mKdV Equations
    Published:
    25 November 2017

    DOI: https://doi.org/10.1007/978-3-642-27737-5_305-3

  2. Original

    Korteweg-de Vries Equation (KdV) and Modified Korteweg-de Vries Equations (mKdV), Semi-analytical Methods for Solving the
    Published:
    25 June 2014

    DOI: https://doi.org/10.1007/978-3-642-27737-5_305-2

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