Type [formula omitted] reduced nonlocal integrable mKdV equations and their soliton solutions

Abstract

A kind of novel reduced nonlocal integrable mKdV equations of odd order is presented by taking two group reductions of the AKNS matrix spectral problems. One reduction is local, replacing the spectral parameter with its negative and the other is nonlocal, replacing the spectral parameter with its negative complex conjugate. Based on distribution of eigenvalues, soliton solutions are generated from the corresponding reflectionless Riemann–Hilbert problems.