Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation

Abstract

In this paper, we propose an integrable fractional derivative nonlinear Schrödinger (fDNLS) equation with the aid of the completeness of the squared eigenfunctions for the Kaup–Newell system. Then we further construct an appropriate Riemann–Hilbert problem, from which we obtain a reconstruction formula of the solution of the fDNLS equation. The fractional N-soliton solution is carried out explicitly by means of determinants and the fractional one-soliton solution is verified rigorously.