Riemann-Hilbert problems and inverse scattering of nonlocal real reverse-spacetime matrix AKNS hierarchies

We would like to propose a kind of nonlocal real reverse-spacetime integrable hierarchies of PT symmetric matrix AKNS equations through nonlocal symmetry reductions on the potential matrix, and formulate their associated Riemann-Hilbert problems to determine generalized Jost solutions of arbitrary-order matrix spectral problems. The Sokhotski-Plemelj formula is applied in transforming the associated Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. The Riemann-Hilbert problems corresponding to the reflectionless case are solved explicitly, where eigenvalues could equal adjoint eigenvalues, and thus, soliton solutions are presented for the resulting nonlocal real reverse-spacetime integrable PT-symmetric matrix AKNS equations. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study proposes a nonlocal real reverse-spacetime integrable hierarchies of PT symmetric matrix AKNS equations, achieved through nonlocal symmetry reductions on the potential matrix, to determine generalized Jost solutions. By applying the Sokhotski-Plemelj formula, the associated Riemann-Hilbert problems are transformed into integral equations of Gelfand-Levitan-Marchenko type. The Riemann-Hilbert problems corresponding to the reflectionless case are explicitly solved, presenting soliton solutions for the resulting nonlocal real reverse-spacetime integrable PT-symmetric matrix AKNS equations.