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Spectral method for solving the equal width equation based on Chebyshev polynomials

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Abstract

A spectral solution of the equal width (EW) equation based on the collocation method using Chebyshev polynomials as a basis for the approximate solution has been studied. Test problems, including the migration of a single solitary wave with different amplitudes are used to validate this algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The interaction of two solitary waves is seen to cause the creation of a source for solitary waves. Usually these are of small magnitude, but when the amplitudes of the two interacting waves are opposite, the source produces trains of solitary waves whose amplitudes are of the same order as those of the initial waves. The three invariants of the motion of the interaction of the three positive solitary waves are computed to determine the conservation properties of the system. The temporal evaluation of a Maxwellian initial pulse is then studied. Comparisons are made with the most recent results both for the error norms and the invariant values.

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  1. Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt

    A. H. A. Ali

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  1. A. H. A. Ali
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Ali, A.H.A. Spectral method for solving the equal width equation based on Chebyshev polynomials. Nonlinear Dyn 51, 59–70 (2008). https://doi.org/10.1007/s11071-006-9191-0

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  • DOI: https://doi.org/10.1007/s11071-006-9191-0

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