Nonlinear water waves (KdV) equation and Painleve technique

  • Authors

    • Attia Mostafa Faculty of Mathematics, University of Belgrade
  • Kortewege-de Vrise equation, Painleve property, Resonance points, Exact solutions.
  • 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.