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

Abstarct We 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.

Automated summary

In this paper, a class of novel reduced nonlocal reverse-spacetime integrable modified Korteweg-de Vries equations is presented through two group reductions of the Ablowitz-Kaup-Newell-Segur matrix spectral problems. Soliton solutions are generated from the reflectionless Riemann-Hilbert problems by taking advantage of the distribution of eigenvalues, where eigenvalues could equal adjoint eigenvalues.