Type (λ⁎,λ) reduced nonlocal integrable AKNS equations and their soliton solutions

Abstract

We construct a class of novel reduced nonlocal reverse-spacetime integrable AKNS equations by taking two group reductions of the AKNS matrix spectral problems of arbitrary order. One reduction is local, replacing the spectral parameter with its complex conjugate while the other is nonlocal, replacing the spectral parameter with itself. Then based on the specific distribution of eigenvalues, we compute soliton solutions by using the Riemann-Hilbert problems with the identity jump matrix, where eigenvalues could equal adjoint eigenvalues.