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Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schr\'odinger equations
- Source :
- Chaos 32, 123110 (2022)
- Publication Year :
- 2022
-
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.<br />Comment: 14 pages, 4 figures
Details
- Database :
- arXiv
- Journal :
- Chaos 32, 123110 (2022)
- Publication Type :
- Report
- Accession number :
- edsarx.2208.04493
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1063/5.0101921