  We consider a dual-core nonlinear waveguide with the parity-time (PT)
symmetry, realized in the form of equal gain and loss terms carried by the
coupled cores. To expand a previously found stability region for solitons in
this system, and explore possibilities for the development of dynamical control
of the solitons, we introduce "management" in the form of periodic sinusoidal
variation of the loss-gain (LG) coefficients, along with synchronous variation
of the inter-core coupling (ICC) constant. This system, which can be realized
in optics (in the temporal and spatial domains alike), features strong
robustness when amplitudes of the variation of the LG and ICC coefficients keep
a ratio equal to that of their constant counterparts, allowing one to find
exact solutions for PT-symmetric solitons. A stability region for the solitons
is identified in terms of the management amplitude and period, as well as the
soliton's amplitude. In the long-period regime, the solitons evolve
adiabatically, making it possible to predict their stability boundaries in an
analytical form. The system keeping the Galilean invariance, collisions between
moving solitons are considered too.
