Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schr\"odinger equations

Weifang Weng; Minghe Zhang; Zhenya Yan

doi:10.1063/5.0101921

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arXiv · 2208.04493

Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schr\"odinger equations

Weifang Weng·Minghe Zhang·Zhenya Yan

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Abstract

In this paper, we explore the anomalous dispersive relations, inverse scattering transform and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Schrodinger (fHONLS) equations, containing the fractional Hirota (fHirota), fractional complex mKdV (fcmKdV), and fractional Lakshmanan-Porsezian-Daniel (fLPD) 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 fHirota and fcmKdV equations. The wave, group, and phase velocities of these envelope fractional 1-soliton solutions are related to the power laws of their amplitudes. These obtained fractional N-soliton solutions may be useful to explain the related super-dispersion transports of nonlinear waves in fractional nonlinear media.

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BibTeX RIS

Weifang Weng, Minghe Zhang, Zhenya Yan. 2022-08-09. Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schr\"odinger equations. https://doi.org/10.1063/5.0101921

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