  In this paper, we use a traveling wave reduction or a so-called spatial
approximation to comprehensively investigate periodic and solitary wave
solutions of the modified Benjamin, Bona & Mahony equation (BBM) to include
both dissipative and dispersive effects of viscous boundary layers. Under
certain circumstances that depend on the traveling wave velocity, classes of
periodic and solitary wave like solutions are obtained in terms of Jacobi
elliptic functions. An ad-hoc theory based on the dissipative term is
presented, in which we have found a set of solutions in terms of an implicit
function. Using dynamical systems theory we prove that the solutions of
\eqref{BBMv} experience a transcritical bifurcation for a certain velocity of
the traveling wave. Finally, we present qualitative numerical results.
