Families of stationary modes in complex potentials

It is shown that a general class of complex asymmetric potentials of the form $w^2(x)-i{w}_x(x)$, where $w(x)$ is a real function, allows for the existence of one-parametric continuous families of the stationary nonlinear modes bifurcating from the linear spectrum and propagating in Kerr media. As an example, we introduce an asymmetric double-hump complex potential and show that it supports continuous families of stable nonlinear modes.