  A double-channel waveguide with gain and loss is addressed and the
corresponding coupled-mode equations are established by employing the coupled
mode approach. Based on the coupled-mode equations, the beam dynamics in the
double-channel waveguide with gain and loss is investigated, and the results
show that there exist three distinct dynamical behaviors, which are
amplification, attenuation to zero and tending to a steady value (or
equilibrium state), respectively. Finally, it is shown that the theoretical
results suggested by the coupled-mode equations agree well with the numerical
simulations.
