The Behavior of Nonlinear Tsunami Waves Running on the Shelf

The problem of creating methods for calculating tsunami parameters and predicting these dangerous events is currently being solved by integrating the equations of the theory of water waves. Both numerical methods and powerful computers are used, as well as analytical solutions. The essential stage is the stage of the tsunami reaching the shelf and shallow coastal waters. The tsunami amplitude increases here, and nonlinear effects become important. Nonlinearity excludes the solution’s unicity and the superposition principle’s fulfillment. The nonlinear theory can have many solutions, depending on various external conditions; there could be nontrivial ones. In this article, we explore the properties of several nonlinear solutions. With their help, we can find the maximum possible amplitude of tsunami waves when approaching the coast and estimate the seismological parameters of an earthquake-generating tsunami.