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

BPS Submodels of The Generalized Skyrme Model and How to Find Them