Bright solitary waves in high dispersive media with parabolic nonlinearity law: The influence of third order dispersion

Abstract We find exact bright solitary wave solutions of a cubic-quintic nonlinear Schrodinger equation describing the propagation of extremely short pulses. Particular cases are discussed. The influence of third order dispersion is numerically investigated, showing the pulse stability for relative low values of the third order dispersion coefficient. When propagation at the zero dispersion point is considered the pulses are always unstable.