Abstract

In this talk, we explore the anomalous dispersive relations, inverse scattering transform, and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Schrödinger equations. 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 in the reflectionless case.