Bifurcation of Soliton Families from Linear Modes in Non-PT-Symmetric Complex Potentials

Continuous families of solitons in the nonlinear Schrodinger equation with non-PT-symmetric complex potentials and general forms of nonlinearity are studied analytically. Under a weak assumption, it is shown that stationary equations for solitons admit a constant of motion if and only if the complex potential is of a special form g2(x)+ig(x), where g(x) is an arbitrary real function. Using this constant of motion, the second-order complex soliton equation is reduced to a new second-order real equation for the amplitude of the soliton. From this real soliton equation, a novel perturbation technique is employed to show that continuous families of solitons bifurcate out from linear discrete modes in these non-PT-symmetric complex potentials. All analytical results are corroborated by numerical examples.