Reduced nonlocal integrable mKdV equations of type (−λ, λ) and their exact soliton solutions

Abstract

AbstarctWe conduct two group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems to present a class of novel reduced nonlocal reverse-spacetime integrable modified Korteweg–de Vries equations. One reduction is local, replacing the spectral parameter with its negative and the other is nonlocal, replacing the spectral parameter with itself. Then by taking advantage of distribution of eigenvalues, we generate soliton solutions from the reflectionless Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues.