INTRODUCTION

Nonlinear optical pulses can propagate in dispersive fibers in the form of bright and dark solitons under certain conditions, as first described by Zakharov and Shabat in 1972[#ZA##1###] and in 1973,[#ZB##1###] respectively. They are stationary solutions of the initial boundary value problem of the nonlinear Schr<#398#>#math218##tex2html_wrap_inline1958#<#398#>dinger equation (NLSE).[#SA##1###]

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In the anomalous dispersion regime of the fiber, under the boundary condition #math219#u(z, t = ±∞) = 0, there exists a class of particle-like, stationary solutions called bright solitons.[#HA##1###] In the normal dispersion region, under the boundary condition #math220#| u(z, t = ±∞)| =constant, one can obtain another class of stationary solutions, which are called dark solitons, since a dip occurs at the center of the pulse.[#HB##1###] ...

In the following discussions, we adopt the normalization convention used in Agrawal's book.[#AB##1###] We normalize the field amplitude A (optical power P0 = A2) into u by

#math221#
u = #tex2html_wrap_indisplay1966#2πn2τ02#tex2html_wrap_indisplay1969#λAeff| β2|#tex2html_wrap_indisplay1970#A,      

where #math222#Aeff is the effective area of the propagating mode, #math223#n2 = 3.2×10-16cm2/W is the nonlinear optical Kerr coefficient of the silica fiber, and β2 is a parameter describing the group velocity dispersion of fiber, ...