  We introduce a parametrically driven Ginzburg-Landau (GL) model, which admits
a gradient representation, and is subcritical in the absence of the parametric
drive (PD). In the case when PD acts uniformly in space, this model has a
stable kink solution. A nontrivial situation takes places when PD is itself
subject to a kink-like spatial modulation, so that it selects real and
imaginary constant solutions at +infinity and -infinity. In this situation, we
find stationary solutions numerically, and also analytically for a particular
case. They seem to be of two different types, viz., a pair of kinks in the real
and imaginary components, or the same with an extra kink inserted into each
component, but we show that both belong to a single continuous family of
solutions. The family is parametrized by the coordinate of a point at which the
extra kinks are inserted. Solutions with more than one kink inserted into each
component do not exist. Simulations show that the former solution is always
stable, and the latter one is, in a certain sense, neutrally stable, as there
is a special type of small perturbations that remain virtually constant in
time, rather than decaying or growing (they eventually decay, but extremely
slowly).
