Numerical experiments for long nonlinear internal waves via Gardner equation with dual-power law nonlinearity

Turgut Ak ()
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Turgut Ak: Armutlu Vocational School, Yalova University, 77500 Yalova, Turkey

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 09, 1-18

Abstract: This paper studies Gardner equation, which represents long nonlinear internal waves. The collocation method based on B-splines is applied to the equation. The stability of the proposed numerical scheme is analyzed by using von Neumann theory. To observe some physical properties of long nonlinear internal waves, three test problems which contain the propagation of solitary waves, the interaction of solitary waves and evolution of solitons are considered. Also, the effect of nonlinearity on physical problems is investigated. In order to see this effect clearly, the same parameters are used during the computation for different degrees of nonlinearity in each problem.

Keywords: Gardner equation; collocation; solitary waves; internal waves; B-spline (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0129183119500669

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