Abstract
We obtain the exact bright and dark solitary wave solutions of the nonlinear Schrödinger equation (NLSE) with the higher-order nonlinearity and the third-order dispersion without any specified conditions, and analyze the features of the solutions. The results show that the higher-order nonlinearity and the third-order dispersion can mutually compensate for a soliton just as the usual self-phase modulation (SPM) and the group-velocity dispersion (GVD) in the NLSE; whether a bright or dark soliton exists in a monomode optical fiber is determined by the sign of the third-order dispersion instead of the group velocity dispersion; the peak intensity of the soliton is proportional to the ratio of the third-order dispersion and the higher-order nonlinearity; the velocity of the soliton depends on the soliton width η, so no bound N-soliton states exist.
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