Nonlinear water waves (KdV) equation and Painleve technique

  • Authors

    • Attia Mostafa Faculty of Mathematics, University of Belgrade

    How to Cite

    Mostafa, A. (2015). Nonlinear water waves (KdV) equation and Painleve technique. International Journal of Basic and Applied Sciences, 4(2), 216-223. https://doi.org/10.14419/ijbas.v4i2.2708

    Received date: May 6, 2014

    Accepted date: June 7, 2014

    Published date: May 4, 2015

    https://doi.org/10.14419/ijbas.v4i2.2708
  • Kortewege-de Vrise equation, Painleve property, Resonance points, Exact solutions.

  • Abstract

    The Korteweg-de Vries (KdV) equation which is the third order nonlinear PDE has been of interest since Scott Russell (1844) . In this paper we study this kind of equation by Painleve equation and through this study, we find that KdV equation satisfies Painleve property, but we could not find a solution directly, so we transformed the KdV equation to the like-KdV equation, therefore, we were able to find four exact solutions to the original KdV equation.

  • References

    1. [1]- A. Alderani, "Painlev'e analysis and Lie symmetries of some nonlinear PDEs", Ph.D thesis, Istanbul Technical University,Turkey (1996).

      [2]- A. Ali, "Finite element studies of the Korteweg-de Vries equation", Ph.D thesis in mathematics. University of Wales, UK (1989).

      [3]- A. Mostafa, "Some solutions of the modified Korteweg-de Vries equation by Painleve test", International Proceedings of Computer Science and Information Technology, Vol.59, (2014), pp.105-111.

      [4]- D. Baldwin, Symbolic algorithms and software for the Painleve test and recursion operators for nonlinear partial differential equations, master thesis, Mathematical and Computer Sciences, Golden School, Colorado, USA, (2004).

      [5]- K. Brauer, The KdV equation: History, exact solutions, and graphical representation, University of Osnabruck, Applied Systems Science, Germany, (2006).

      [6]- W. Hereman, "Shallow water waves and solitary waves", Mathematics of Complexity and Dynamical Systems, (2011), pp.1520-1532.

      [7]- W. Steep and N. Euler, Nonlinear Evolution Equations and Painleve Test, World Scientific Publishing Co. Pte. Ltd, (1988).

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  • How to Cite

    Mostafa, A. (2015). Nonlinear water waves (KdV) equation and Painleve technique. International Journal of Basic and Applied Sciences, 4(2), 216-223. https://doi.org/10.14419/ijbas.v4i2.2708

    Received date: May 6, 2014

    Accepted date: June 7, 2014

    Published date: May 4, 2015