Journal of Nonlinear Science

, Volume 10, Issue 1, pp 1–22 | Cite as

Numerical Solution of Some Nonlocal, Nonlinear Dispersive Wave Equations

  • B. Pelloni
  • V. A. Dougalis


We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.


Solitary Wave Euler Equation Initial Angle Initial Contour Vortex Method 
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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • B. Pelloni
    • 1
  • V. A. Dougalis
    • 2
  1. 1.Department of Mathematics, Imperial College of Science, Technology and Medicine, London SW7 2BZ, UKUK
  2. 2.Department of Mathematics, University of Athens, Panepistemiopolis, Zographou 15784, GreeceGreece

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