Solitary wave solutions and their velocity selections and prohibitions for a general Boussinesq type fluid model
The possible solitary wave solutions for a general Boussinesq (GBQ) type fluid model are studied analytically. After proving the non-Painlevé integrability of the model, the first type of exact explicit travelling solitary wave with a special velocity selection is found by the truncated Painlevé 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.