Soliton resulting from the combined effect of higher order dispersion, self-steepening and nonlinearity in an optical fiber

A soliton with a nonvanishing boundary condition is found for The generalized nonlinear Schrodinger equation under the condition beta(2)/beta(3) = omega(0)/2 (beta(2) the second Order dispersion, beta(3) is the third order dispersion, omega(0) is the carrier frequency) neglecting the terms concerned with loss and retarded nonlinear response. In the normal dispersion regime, dark solitons exist, however in the anomalous dispersion regime, bright solitons exist superimposed on the continuous wave background, and especially in the long wave limit rational solitons also exist.