Exact kink solitons in Skyrme crystals

We present an explicit integration of the kink soliton equation obtained in a recent interesting study of the classical Skyrme model where the field configurations are of a generalized hedgehog form which is of a domain-wall type. We also show that in such a reduced one-dimensional setting the first-order and second-order equations are equivalent. Consequently, in such a context, all finite-energy solitons are Bogomolnyi-Prasad-Sommerfield type and precisely known.