PAINLEVE ANALYSIS AND BRIGHT SOLITARY WAVES OF THE HIGHER-ORDER NONLINEAR SCHRODINGER-EQUATION CONTAINING 3RD-ORDER DISPERSION AND SELF-STEEPENING TERM

A general form of the higher-order nonlinear Schrodinger equation that includes terms accounting for the third-order dispersion and the self -steepening effect has been investigated using the Painleve singularit y structure analysis in order to identify the underlying integrable mo dels. This equation fails to pass the Painleve test for the entire par ameter space except for two specific choices of the parameters. As a c onsequence, it was found that two recently introduced higher-order non linear Schrodinger equations fail to pass the Painleve integrability t est. Moreover, one of those equations describes optical pulses with la rge 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 introduce d and bright solitary waves are provided. These solitary waves describ e pulses with either very small or even zero-frequency shifts. The con ditions on fiber parameters for the existence of those solitary waves are also discussed.