  This work deals with defect structures in models described by scalar fields.
The investigations focus on generalized models, with the kinetic term modified
to allow for a diversity of possibilities. We develop a new framework, in which
we search for first-order differential equations which solve the equations of
motion. The main issue concerns the introduction of a new function, which works
like the superpotential usually considered in the standard situation. We
investigate the problem in the general case, with an arbitrary number of
fields, and we present several explicit examples in the case of a single real
scalar field.
