  Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain
and loss distributions still possess all-real linear spectrum or exhibit phase
transition. In this article, nonlinear light behaviors in these complex
waveguides are probed analytically near a phase transition. Using multi-scale
perturbation methods, a nonlinear ordinary differential equation (ODE) is
derived for the light's amplitude evolution. This ODE predicts that the first
class of these non-PT-symmetric waveguides support continuous families of
solitons and robust amplitude-oscillating solutions both above and below phase
transition, in close analogy with PT-symmetric systems. For the other classes
of waveguides, the light's intensity always amplifies under the effect of
nonlinearity even if the waveguide is below phase transition. These analytical
predictions are confirmed by direct computations of the full system.
