(7) On controlled propagation of nonautonomous dispersive coupled Whitham–Broer–Kaup equation in shallow water

M. Tantawy
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

Received 2 July 2017; accepted 8 August 2017
Available online 24 August 2017

Abstract
In this paper, the dispersive coupled Whitham–Broer–Kaup (DCWBK) equation with time-dependent coefficients describing the propagation of the shallow water waves are obtained. The propagation of solitons and elliptic (or chirped) waves can be manipulated by suitable variations of the dispersion coefficient. Here, controllable transmission of the surface waves for soliton similariton pairs with the snoidal backgrounds is considered. It is found that, when the dispersion coefficient is taken as increasing, the velocity is increasing with the dispersion coefficient increasing. While this holds vice versa for the height of propagation wave.
© 2017 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
Keywords: Dispersive coupled Whitham–Broer–Kaup (DCWBK) equation; Unified method (UM); Dispersion coefficient; Controlled.