Nonlocal integrable mKdV equations by two nonlocal reductions and their soliton solutions

Abstract

We conduct two nonlocal group reductions of the AKNS matrix spectral problems to generate a class of nonlocal reverse-spacetime integrable mKdV equations. One reduction replaces the spectral parameter with its negative complex conjugate while the other does not change the spectral parameter. Beginning with the specific distribution of eigenvalues, we construct soliton solutions by solving the corresponding generalized Riemann-Hilbert problems with the identity jump matrix, where eigenvalues could equal adjoint eigenvalues.