Numerical Study of Traveling Wave Solutions to 2D Boussinesq Equation

Abstract

The aim of this paper is to evaluate stationary propagating wave solutions to the two dimensional Boussinesq equation. To solve the resulting nonlinear fourth order elliptic problem we use a combination of high order finite difference schemes, an iterative procedure and new asymptotic boundary conditions. A number of numerical results are obtained for the validation of the method and for the dependence of the wave's shape on the velocity c and dispersion parameters. We also give a comparison with the numerical results and best-fit formulae given in [4, 5].