Optical solitary wave and shock solutions of the higher order nonlinear Schrodinger equation

An exact analytical solution describing the evolution of nonlinear optical envelope pulses in an optical fiber is obtained. The propagation of the pul se is modeled by a higher order nonlinear Schrodinger equation containing t hird order and nonlinear dispersive terms. This solution includes pulses th at are symmetric solitary waves, asymmetric solitary waves, and asymmetric structures that develop into an optical shock.