Eur. Phys. J. Plus (2022) 137: 404
https://doi.org/10.1140/epjp/s13360-022-02620-y

Regular Article

Inverse scattering of nonlocal Sasa–Satsuma equations and their multisoliton solutions

Department of Mathematics, Harbin Institute of Technology, 150001, Harbin, People’s Republic of China

^c bohan@hit.edu.cn

Received: 18 October 2021
Accepted: 18 March 2022
Published online: 30 March 2022

Abstract

We study the nonlocal Sasa–Satsuma equations which include the reverse-space, reverse-time, and reverse-spacetime nonlocal Sasa–Satsuma equations under nonlocal group reductions of the Ablowitz–Kaup–Newell–Segur hierarchy. We analyze the inverse scattering transforms of the nonlocal Sasa–Satsuma equations by constructing a class of associated Riemann–Hilbert problems to matrix spectral problems, and the Sokhotski Plemelj formula is used to transform the Riemann–Hilbert problems into Gelfand–Levitan–Marchenko-type integral equations. In addition, we give a solution formulation to the Riemann–Hilbert problems. Finally, under the reflectionless transforms, we construct the corresponding multisoliton solutions for the nonlocal Sasa–Satsuma equations.