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Higher order dispersive effects in regularized Boussinesq equation
Institution:1. Istanbul Technical University, Department of Mathematics, Maslak 34469, Istanbul, Turkey;2. Istanbul Kemerburgaz University, Department of Basic Sciences, Bagcilar 34217, Istanbul, Turkey;1. Department of Applied Mathematics, University of Valladolid, Paseo del Cauce 59, 47011-Valladolid, Spain;2. IMUVA, Institute of Mathematics of University of Valladolid, Spain;3. Department of Applied Mathematics, University of Valladolid, Paseo de Belén 15, 47011-Valladolid, Spain;1. Department of Basic Sciences, Istanbul Kemerburgaz University, Bagcilar, Turkey;2. Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen, Norway;3. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, United States;1. F?rat University, Science Faculty, Department of Mathematics, 23119, Elazig, Turkey;2. Cankaya University, Department of Mathematics, Ogretmenler Street, 1406530, Ankara, Turkey;3. Institute of Space Sciences, Magurele, Bucharest, Romania;1. Department of Applied Mathematics, University of Valladolid, Paseo del Cauce 59, 47011, Valladolid, Spain;2. IMUVA, Institute of Mathematics of University of Valladolid, Spain;3. Department of Applied Mathematics, University of Valladolid, Paseo de Belen 15, 47011 Valladolid, Spain
Abstract:In this paper, we consider the higher order Boussinesq (HBq) equation which models the bi-directional propagation of longitudinal waves in various continuous media. The equation contains the higher order effects of frequency dispersion. The present study is devoted to the numerical investigation of the HBq equation. For this aim a numerical scheme combining the Fourier pseudo-spectral method in space and a Runge–Kutta method in time is constructed. The convergence of semi-discrete scheme is proved in an appropriate Sobolev space. To investigate the higher order dispersive effects and nonlinear effects on the solutions of HBq equation, propagation of single solitary wave, head-on collision of solitary waves and blow-up solutions are considered.
Keywords:The higher-order Boussinesq equation  Fourier pseudo-spectral method  Solitary waves  Head-on collision of solitary waves  Blow-up
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