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In this work we consider the higher dimensional Skyrme model, with spatialdimension $d > 3$, focusing on its BPS submodels and their correspondingfeatures. To accommodate the cases with a higher topological degree, $B\geq1$, a modified generalized hedgehog ansatz is used where we assign an integer$n_i$ for each rotational plane, resulting in a topological degree thatproportional to product of these integers. It is found via BPS Lagrangianmethod that there are only two possible BPS submodels for this sphericallysymmetric ansatz which shall be called as BPS Skyrme model and scale-invariantmodel. The properties of the higher dimensional version of both submodels arestudied and it is found that the BPS Skyrmions with $B\geq1$ exist in thefirst submodel but there is only $B=1$ BPS Skyrmion in the second submodel.We also study the higher dimensional version of self-duality conditions interms of strain tensor eigenvalues and find that, in general, thescale-invariant model has a stronger self-duality condition than the BPS Skyrmemodel.

BPS Skyrmions of Generalized Skyrme Model In Higher Dimensions