A comparison between analytical and numerical simulations of solutions of the coupled Boussinesq equations

The results of an analytical formulation and a numerical model of solitary wave solutions of the coupled Boussinesq equations are compared over variable and constant water depths. A brief description on the analytical and numerical model is presented. The input values of the analytical model for surface elevation and velocity profiles are used in the numerical model. The simulations for surface and velocity profiles of the solitary wave solutions are compared over variable depths. Further, the velocity profiles of the coupled and generalized coupled Boussinesq equations are compared against analytical solutions. It is observed that the surface and velocity amplitudes are in good agreement with their peak values and also the patterns of the wave propagation are very similar in nature in case of one-dimensional Boussinesq equation. The velocity amplitude and the behaviour of the profiles of the solitary wave are close to the analytical results.