Abstract
In the present work the propagation of bright solitons under the influence of third-order of linear dispersion and self-steepening effect in single-mode fibers is analytically studied. Such optical pulses can be observed as a result of the dynamic balance between higher orders of dispersive and nonlinear phenomena. New analytical solutions of the nonlinear amplitude equation (NAE) in the form of cnoidal waves are found. The solutions are presented by Jacobi elliptic delta functions. It is shown that at certain values of the parameter
k
, representing modulus of ellipticity, the solutions can be reduced to
sech
-soliton.