Existence threshold for the ac-driven damped nonlinear Schrodinger solitons

It has been known for some time that solitons of the externally driven, dam ped nonlinear Schrodinger equation can only exist if the driver's strength, h, exceeds approximately (2/pi)gamma, where gamma is the dissipation coeff icient. Although this perturbative result was expected to be correct only t o the leading order in gamma, recent studies have demonstrated that the for mula h(thr) = (2/pi)gamma gives a remarkably accurate description of the so liton's existence threshold prompting suggestions that it is, in fact, exac t. In this note we evaluate the next order in the expansion of h(thr)(gamma ) showing that the actual reason for this phenomenon is simply that the nex t-order coefficient is anomalously small: h,h, = (2/pi)gamma + 0.002 gamma( 3). Our approach is based on a singular perturbation expansion of the solit on near the turning point; it allows to evaluate h(thr) (gamma) to all orde rs in gamma and can be easily reformulated for other perturbed soliton equa tions. (C) 1999 Elsevier Science B.V. All rights reserved.