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