Study tsunamis through approximate solution of damped geophysical Korteweg-de Vries equation

The article studied tsunami waves with consideration of important wave properties such as velocity, width, and collision through finding an approximate solution to the damped geophysical Korteweg-de Vries (dGKdV). The addition of the damping term in the GKdV is a result of studying the nonlinear waves in bounded nonplanar geometry. The properties of the wave in bounded nonplanar geometry are different than the unbounded planar geometry, as many experiments approved. Thus, this work reported for the first time the analytical solution for the dGKdV equation using the Ansatz method. The used method assumed a suitable hypothesis and the initial condition of the GKdV. The GKdV is an integrable equation and the solution can be found by several known methods either analytically or numerically. On the other hand, the dGKdV is a nonintegrable equation and does not have an initial exact solution, and this is the challenge. In this work, the novel Ansatz method proved its ability to reach the approximate solution of dGKdV and presented the effect of the damping term as well as the Coriolis effect term in the amplitude of the wave. The advantage of the Ansatz method was that the obtained solution was in a general solution form depending on the exact solution of GKdV. This means the variety of nonlinear wave structures like solitons, lumps, or cnoidal can be easily investigated by the obtained solution. We realized that the amplitude of a tsunami wave decreases if the Coriolis term or damping term increases, while it increases if wave speed increases.