  This work deals with the presence of topological structures in models of two
real scalar fields in the two-dimensional spacetime. The subject concerns the
presence of a geometric constriction, which appears with a modification of the
kinetic term of one of the two fields. We elaborate on the construction of a
first-order framework, which directly contributes to find analytical solutions.
We describe several distinct possibilities, in particular, the case where the
first-order equations do not separate. This is much harder, but we use the
integrating factor to deal with analytical configurations. The proposed
methodology help us deal with localized structures of both the N\'eel and Bloch
type very naturally, and we end the work suggesting some possibilities of
applications in distinct areas of nonlinear science.
