Abstract
This paper addresses the dynamics of dispersive shallow water wave that is governed by the Rosenau–KdV equation with power law nonlinearity. The singular 1-soliton solution is derived by the ansatz method. Subsequently, the soliton perturbation theory is applied to obtain the adiabatic parameter dynamics of the water waves. Finally, the integration of the perturbed Rosenau–KdV equation is obtained by the ansatz method as well as the semi-inverse variational principle.
► Dispersive shallow water waves ocean shore is studied by the Rosenau–KdV equation. ► Soliton perturbation theory is applied and fixed value of amplitude is obtained. ► The perturbed Rosenau–KdV equation is integrated. ► The singular soliton solutions are obtained.