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We investigate exact travelling wave solutions of higher order nonlinearSchrodinger equation in the absence of third order dispersion, which exhibitnon-trivial self phase modulation. It is shown that, the correspondingdynamical equation, governing the evolution of intensity in the femtosecondregime, is that of non-linear Schrodinger equation with a source. The exactlocalized solutions to this system can have both super and subluminalpropagation belonging to two distinct class. A number of these solitons exhibitchirality, thereby showing preferential propagation behavior determined bygroup velocity dispersion. Both localized bright and dark solitons are found incomplementary velocity and experimental parameter domains, which can exist foranomalous and normal dispersion regimes. It is found that, dark solitons inthis system propagate with non-zero velocity, unlike their counterpart innanosecond regime. Interestingly, subluminal propagation is observed forsolitons having a nontrivial Pade type intensity profile.

Travelling wave solutions to nonlinear Schrodinger equation with self-steepening and self-frequency shift