  Using the BPS Lagrangian method we show that all known BPS submodels of the
generalized Skyrme model, with a particular ansatz for the fields content, can
be devided into three groups based on the (effective) number of
derivative-terms in the BPS submodels. We are able to derive rigorously the
Bogomolny's equations of those BPS submodels. The resulting Bogomolny's
equations, along with possible constraint equations, are in general forms in
which some of the known BPS submodels may contain other possible non-trivial
(non-vacuum) solutions then the ones found in the literature. Furthermore, we
derive some other new BPS submodels of the generalized Skyrme model for each of
the groups and some of them yield new solutions.
