Modeling of the solitary waves trajectories in “shallow water” environme

Abstract

Solitary waves in the “shallow water” environment are considered and approximate approach to calculation and prediction of trajectories of these waves is proposed. We use an approach which was developed in recent years and was called the T-representations method. This method allows to move away from the exact solutions of the corresponding systems of differential equations and construct the trajectory approximately, in fact estimating only the point of maximum of the wave amplitude and its displacement. An appropriate mathematical simplification makes efficient computer simulations possible. In recent years, software packages have been actively used to monitor and predict a number of dangerous natural phenomena, such as Earth Alerts, Pacific Tsunami Warning System, Wave Monitoring Sites and others. But these systems do not take solitary waves into account. Using our approach, it is possible to refine the parameters of solitary waves in a specific environment, investigate whether such waves exist there at all and create functions taking into account solitary waves in monitoring systems.