  We study dynamical and stationary states of solitons in dual-core waveguides
which are locally coupled (fused) at one or several short segments. The model
applies to planar optical waveguides, and to BEC in dual traps. Collisions of
an incident soliton with single and double locally-fused couplers are
investigated by means of systematic simulations and several analytical methods
(quasi- linear, fast-soliton, and adiabatic approximations). Excitation
dynamics of a soliton trapped by a local coupler is studied by means of the
variational approximation, and verified by simulations. Shuttle motion of a
soliton trapped in a cavity between two local couplers, and in a finite array
of couplers, is studied too.
