Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation

In this paper, we propose an integrable fractional derivative nonlinear Schrodinger (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. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.