  A dual-core waveguide with balanced gain and loss in different arms and with
intermodal coupling is considered. The system is not invariant under the
conventional $PT$ symmetry but obeys $CPT$ symmetry where an additional spatial
inversion $C$ corresponds to swapping the coupler arms. We show that
second-order dispersion of coupling allows for unbroken $CPT$ symmetry and
supports propagation of stable vector solitons along the coupler.
Small-amplitude solitons are found in explicit form. The combined effect of
gain-and-loss and dispersive coupling results in several interesting features
which include a separation between the components in different arms, nontrivial
dependence of stability of a soliton on its velocity, and the existence of more
complex stationary two-hump solutions. Unusual decay dynamics of unstable
solitons is discussed too.
