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.
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