  The possible solitary wave solutions for a general Boussinesq (GBQ) type
fluid model are studied analytically. After proving the non-Painlev\'e
integrability of the model, the first type of exact explicit travelling
solitary wave with a special velocity selection is found by the truncated
Painlev\'e expansion. The general solitary waves with different travelling
velocities can be studied by casting the problems to the Newtonian
quasi-particles moving in some proper one dimensional potential fields. For
some special velocity selections, the solitary waves possess different shapes,
say, the left moving solitary waves may possess different shapes and/or
amplitudes with those of the right moving solitons. For some other velocities,
the solitary waves are completely prohibited. There are three types of GBQ
systems (GBQSs) according to the different selections of the model parameters.
For the first type of GBQS, both the faster moving and lower moving solitary
waves allowed but the solitary waves with"middle" velocities are prohibit. For
the second type of GBQS all the slower moving solitary waves are completely
prohibit while for the third type of GBQS only the slower moving solitary waves
are allowed.
