Application of KdV Equations in Policy-Making for Extreme Wave and Tsunami Predictions in Vulnerable Societies

Abstrak

This study aims to examine the possibility of implementing the KdV equations for policymaking in vulnerable communities. It is crucial as Indonesia is located between two continents and two large oceans, significantly influencing marine phenomena, such as the frequent occurrence of extreme waves. Additionally, seismic activity can cause earthquakes with the potential to trigger tsunamis. Therefore, continuous research on extreme waves and tsunamis is required. This research provides a semi-analytical solution to the KdV equation using disturbance parameters, carried out from the first to the seventh order, to generate maximum waves. In this study, the modified KdV equation considers the bichromatic wave input , 2 wavenumber expansion equations using perturbation theory and Taylor series, and η expansion using perturbation theory to produce a seventh-order solution. This solution differs from third-order and fifth-order solutions in the context of higher-order influences, with the peak distance found to be closer than the initial point. It may indicate that the higher-order effects of the solution influence the maximum peak of the wave. The results of this research contribute to a progressive step in helping communities vulnerable to extreme waves and tsunamis.