The existence of stationary solitary waves in symmetric and non-symmetric complex potentials
is studied by means of Melnikov’s perturbation method. The latter provides analytical conditions
for the existence of such waves that bifurcate from the homogeneous nonlinear modes of the system
and are located at specific positions with respect to the underlying potential. It is shown that the
necessary conditions for the existence of continuous families of stationary solitary waves, as they arise
from Melnikov theory, provide general constraints for the real and imaginary part of the potential,
that are not restricted to symmetry conditions or specific types of potentials. Direct simulations
are used to compare numerical results with the analytical predictions, as well as to investigate the
propagation dynamics of the solitary waves.European Union project AEI/FEDER MAT2016-79866-