2D solitary waves of Boussinesq equation

In this paper, the 2D stationary-propagating localized solutions of Boussinesq's equation are investigated numerically. An algorithm for treating the bifurcation and finding a nontrivial solution is created. The scheme is validated employing different grid sizes and different size of the box that contains the solution. The results obtained show that there is pseudo-Lorentzian elongation of the scale of the solitons but it is only in the direction transverse to the propagation velocity. In longitudinal direction the scales are slightly contracted, so kind of "relative" contraction takes place. Results are shown graphically and discussed.