Numerical dynamics of the Generalized Equal Width (GEW) wave equation in presence of high-order nonlinearity

Ali Başhan ()
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Ali Başhan: Zonguldak Bulent Ecevit University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1365-1388

Abstract: Abstract In the present manuscript, Generalized Equal Width (GEW) wave equation which is an alternative model to shallow water wave with high-order nonlinearity is investigated. The GEW equation is solved for cubic, quartic and quintic nonlinear cases, separately. Solitary wave solution of the GEW equation for many applications and interaction of the two waves for two positive amplitudes, two negative amplitudes and one positive and one negative amplitude are solved. It is important to note that interaction of the two negative amplitude waves and interaction of the one positive and one negative wave solutions of the high-order GEW equation are firstly in this study examined. All applications are illustrated. The error norms for the solitary wave solution and the three invariants for all applications are calculated and reported. An illustrative comparison for the newly presented results displays the improvement of the present numerical solution. The rate of the convergence and CPU time is calculated for three different order nonlinear GEW equation.

Keywords: GEW equation; Differential quadrature method; Finite difference method; Convergence; 41A25; 65M06; 65D32; 65D07 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00444-9

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