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This paper is concerned with the study, by computational means, of thegeneration and stability of solitary-wave solutions of generalized versions ofthe Benjamin equation. The numerical generation of the solitary-wave profilesis accurately performed with a modified Petviashvili method which includesextrapolation to accelerate the convergence. In order to study the dynamics ofthe solitary waves the equations are discretized in space with a Fourierpseudospectral collocation method and a fourth-order, diagonally implicitRunge-Kutta method of composition type as time-stepping integrator. Thestability of the waves is numerically studied by performing experiments withsmall and large perturbations of the solitary pulses as well as interactions ofsolitary waves.

Numerical approximation to Benjamin type equations. Generation and stability of solitary waves