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An exact solitary wave solution is presented for the nonlinear Schrodingerequation governing the propagation of pulses in optical fibers including theeffects of second, third and fourth order dispersion. The stability of thissoliton-like solution with sech2 shape is proven by the sign-definiteness ofthe operator and an integral of the Sobolev type. The main criteria governingthe existence of such stable localized pulses propagating in optical fibers arealso formulated. A unique feature of these soliton-like optical pulsespropagating in a fiber with higher order dispersion is that their parameterssatisfy efficient scaling relations. The main soliton solution term given byperturbation theory is also presented when absorption or gain is included inthe nonlinear Schrodinger equation. We anticipate that this type of stablelocalized pulses could find practical applications in communications,slow-light devices and ultrafast lasers.

Solitary Waves in Optical Fibers Governed by Higher Order Dispersion