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• W4313303768 abstract "In this paper, using the algorithm due to Ablowitz et al. [Phys. Rev. Lett. 128, 184101 (2022); J. Phys. A: Math. Gen. 55, 384010 (2022)], we explore the anomalous dispersive relations, inverse scattering transform, and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Schrödinger (fHONLS) equations, containing the fractional third-order NLS (fTONLS), fractional complex mKdV (fcmKdV), and fractional fourth-order nonlinear Schrödinger (fFONLS) equations, etc. The inverse scattering problem can be solved exactly by means of the matrix Riemann-Hilbert problem with simple poles. As a consequence, an explicit formula is found for the fractional N-soliton solutions of the fHONLS equations in the reflectionless case. In particular, we analyze the fractional one-, two-, and three-soliton solutions with anomalous dispersions of fTONLS and fcmKdV equations. The wave, group, and phase velocities of these envelope fractional one-soliton solutions are related to the power laws of their amplitudes. Moreover, we also deduce the formula for the fractional N-soliton solutions of all fHONLS equations and analyze some velocities of the one-soliton solution. These obtained fractional N-soliton solutions may be useful to explain the related super-dispersion transports of nonlinear waves in fractional nonlinear media." @default.
• W4313303768 created "2023-01-06" @default.
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• W4313303768 date "2022-12-01" @default.
• W4313303768 modified "2023-10-03" @default.
• W4313303768 title "Dynamics of fractional <i>N</i>-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations" @default.
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• W4313303768 doi "https://doi.org/10.1063/5.0101921" @default.
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