  This paper is concerned with the study, by computational means, of the
generation and stability of solitary-wave solutions of generalized versions of
the Benjamin equation. The numerical generation of the solitary-wave profiles
is accurately performed with a modified Petviashvili method which includes
extrapolation to accelerate the convergence. In order to study the dynamics of
the solitary waves the equations are discretized in space with a Fourier
pseudospectral collocation method and a fourth-order, diagonally implicit
Runge-Kutta method of composition type as time-stepping integrator. The
stability of the waves is numerically studied by performing experiments with
small and large perturbations of the solitary pulses as well as interactions of
solitary waves.
