Bright optical soliton in the presence of fourth-order dispersion

We show that the generalized nonlinear Schrödinger equation admits of an analytical solution for a bright optical soliton in the presence of fourth-order dispersion. The soliton envelope is expressed as the square of a hyperbolic secant. The peak power and the duration of the soliton are uniquely defined. Numerical simulations tend to show that the temporal shape and the peak power of the soliton are stable when a weak third-order dispersion is introduced.