Inverse scattering transform for the integrable fractional derivative nonlinear Schr?dinger equation

作者：An, Ling; Ling, Liming^*; Zhang, Xiaoen

来源：Physica D: Nonlinear Phenomena , 2024, 458: 133888.

DOI：10.1016/j.physd.2023.133888

• Fractional derivative nonlinear Schrodinger
• equation
• Recursion operator
• Inverse scattering transform
• FractionalN-soliton solution
• Fractional rational solution

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.