Abstract
A general form of the higher-order nonlinear Schr\odinger equation that includes terms accounting for the third-order dispersion and the self-steepening effect has been investigated using the Painlev\'e singularity structure analysis in order to identify the underlying integrable models. This equation fails to pass the Painlev\'e test for the entire parameter space except for two specific choices of the parameters. As a consequence, it was found that two recently introduced higher-order nonlinear Schr\odinger equations fail to pass the Painlev\'e integrability test. Moreover, one of those equations describes optical pulses with large frequency shifts as compared to the chosen carrier frequency that renders that equation inappropriate for describing femtosecond soliton propagation in monomode optical fibers. Another equation is introduced and bright solitary waves are provided. These solitary waves describe pulses with either very small or even zero-frequency shifts. The conditions on fiber parameters for the existence of those solitary waves are also discussed.
Published Version
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