Soliton hierarchies and soliton solutions of type ([formula omitted], [formula omitted] ) reduced nonlocal nonlinear Schrödinger equations of arbitrary even order

Abstract

We present mixed-type reduced soliton hierarchies of nonlocal integrable nonlinear Schrödinger equations of arbitrary even order by conducting two nonlocal group reductions for the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on specific distributions of eigenvalues and adjoint eigenvalues, we construct soliton solutions by solving the corresponding reflectionless generalized Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues.