Numerical Solution of Some Nonlocal, Nonlinear Dispersive Wave Equations |
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Authors: | B Pelloni V A Dougalis |
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Institution: | (1) Department of Mathematics, Imperial College of Science, Technology and Medicine, London SW7 2BZ, UK, GB;(2) Department of Mathematics, University of Athens, Panepistemiopolis, Zographou 15784, Greece, GR |
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Abstract: | Summary. 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.
Received October 28, 1997; revised February 11, 1999; accepted April 7, 1999 |
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