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Solitary wave interactions of the GRLW equation

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  • Ramos, J.I.

Abstract

An approximate quasilinearization method for the solution of the generalized regularized long-wave (GRLW) equation based on the separation of the temporal and spatial derivatives, three-point, fourth-order accurate, compact difference equations, is presented. The method results in a system of linear equations with tridiagonal matrices, and is applied to determine the effects of the parameters of the GRLW equation and initial conditions on the formation of undular bores and interactions/collisions between two solitary waves. It is shown that the method preserves very accurately the first two invariants of the GRLW equation, the formation of secondary waves is a strong function of the amplitude and width of the initial Gaussian conditions, and the collision between two solitary waves is a strong function of the parameters that appear in the GRLW equation and the amplitude and speed of the initial conditions. It is also shown that the steepening of the leading and trailing waves may result in the formation of multiple secondary waves and/or an undular bore; the former interacts with the trailing solitary wave which may move parallel to or converge onto the leading solitary wave.

Suggested Citation

  • Ramos, J.I., 2007. "Solitary wave interactions of the GRLW equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 479-491.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:2:p:479-491
    DOI: 10.1016/j.chaos.2006.01.016
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    1. Soliman, A.A., 2005. "Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(2), pages 119-124.
    2. El-Danaf, Talaat S. & Ramadan, Mohamed A. & Abd Alaal, Faysal E.I., 2005. "The use of adomian decomposition method for solving the regularized long-wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 747-757.
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    Cited by:

    1. Demiray, Hilmi, 2009. "Head-on-collision of nonlinear waves in a fluid of variable viscosity contained in an elastic tube," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1578-1586.
    2. Raslan, K.R., 2009. "Numerical study of the Modified Regularized Long Wave (MRLW) equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1845-1853.
    3. Karakoç, S. Battal Gazi & Zeybek, Halil, 2016. "Solitary-wave solutions of the GRLW equation using septic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 159-171.

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