Existence threshold for the AC-driven damped nonlinear Schroedinger solitons

It has been known for some time that solitons of the externally driven, damped nonlinear Schroedinger equation can only exist if the driver's strength, h, exceeds approximately (2/π)γ, where γ is the dissipation coefficient. Although this perturbative result was expected to be correct only to the leading order in γ, recent studies have demonstrated that the formula hthr = (2/π)γ gives a remarkably accurate description of the soliton's existence threshold prompting suggestions that it is, in fact, exact. In this note we evaluate the next order in the expansion of hthr(γ) showing that the actual reason for this phenomenon is simple that the next-order coefficient is anomalously small: hthr = (2/π)γ + 0.002γ3