A Study on Nonlinear Dispersive Wave Equations and Wave Breaking Solution

Abstract

Nonlinear dispersive wave equations are now widely used to simulate the propagation of shallow water waves. In recent years, it has been clarified that some equations accommodate wave breaking phenomena as well as steady wave solutions. In the present study, comparative studies of the Boussinesq-type equations with different sets of parameters are carried out to investigate the existence of wave breaking solutions. The behavior of solution over the breaking limit is numerically examined using a blowup profile as an indicator of wave breaking. It is found that the solution exhibits the blowup with most sets of parameters for cases with h/L<0.04, while only some specific sets of parameters realize it for shorter waves. Moreover, locations of the blow-up are shown to agree well with actual breaking points known from the empirical criteria.