Small Amplitude Solitons in the Higher Order Nonlinear Schrödinger Equation in an Optical Fibre

By taking advantage of the approximate approach of small amplitude soliton, we study the higher-order nonlinear Schrödinger equation in an optical fibre. Our results show that the bright and dark solitons of small amplitude can appear on the background of a continuous wave in normal dispersion regime or in anomalous dispersion regime simultaneously due to the higher order effects. Interesting connection between the higher-order nonlinear Schrödinger equation and the Korteweg-de Vries equation is also demonstrated.