  We introduce a model of a two-core system, based on an equation of the
Ginzburg-Landau (GL) type, coupled to another GL equation, which may be linear
or nonlinear. One core is active, featuring intrinsic linear gain, while the
other one is lossy. The difference from previously studied models involving a
pair of linearly coupled active and passive cores is that the stabilization of
the system is provided not by a linear diffusion-like term, but rather by a
cubic or quintic dissipative term in the active core. Physical realizations of
the models include systems from nonlinear optics (semiconductor waveguides or
optical cavities), and a double-cigar-shaped Bose-Einstein condensate with a
negative scattering length, in which the active ``cigar'' is an atom laser. The
replacement of the diffusion term by the nonlinear loss is principally
important, as diffusion does not occur in these physical media, while nonlinear
loss is possible. A stability region for solitary pulses is found in the
system's parameter space by means of direct simulations. One border of the
region is also found in an analytical form by means of a perturbation theory.
Moving pulses are studied too. It is concluded that collisions between them are
completely elastic, provided that the relative velocity is not too small. The
pulses withstand multiple tunneling through potential barriers. Robust
quantum-rachet regimes of motion of the pulse in a time-periodic asymmetric
potential are found as well.
