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Mutual compensation of the higher-order nonlinearity and the third-order dispersion. (English) Zbl 0962.35508

Summary: 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 and the group-velocity dispersion 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 \(\eta\), so no bound \(N\)-soliton states exist.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
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