<p>Tsunami waves, which are strong waves, occur in oceans as a result of an earthquake or volcanic eruptions. Tsunamis propagation are described by the geophysical Korteweg–de Vries (geoKdV) equation. To investigate tsunami attenuation, an experimental study examined the impact of coastal vegetation on tsunami waves. The findings indicated that coastal vegetation effectively contributes to the damping of tsunami wave height. However, the dynamics of the interaction between these waves can be mathematically governed by adding an extra term in the geoKdV equation that is the damping term. The damped geoKdV (dgeoKdV) equation is classified as a non-integrable equation, indicating the absence of an exact analytical solution. Consequently, the main goal of this article is to seek a numerical approximation solution for the dgeoKdV equation. For this purpose, we choose one of the powerful numerical methods for solving initial value problems, that is the explicit exponential time differencing method (ETD method). The method utilizes the exact solution of the geoKdV equation as an initial condition to approximate the solution of the dgeoKdV equation. The numerical simulations conducted show the effect of the interaction between the waves and found that the damping term has an effective impact on the amplitude of the tsunami waves. As the values of the damping term increase, the amplitude of the tsunami waves decreases, causing the width of the waves to be flatten. This impact is opposed to the effect of the Coriolis phenomena. Actually, increasing the values of the Coriolis parameter leads to a decrease in the tsunami wave amplitude.</p>