  Historically the finite volume methods have been developed for the numerical
integration of conservation laws. In this study we present some recent results
on the application of such schemes to dispersive PDEs. Namely, we solve
numerically a representative of Boussinesq type equations in view of important
applications to the coastal hydrodynamics. Numerical results of the runup of a
moderate wave onto a non-uniform beach are presented along with great lines of
the employed numerical method (see D. Dutykh et al. (2011) for more details).
