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

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. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

Two nonlocal group reductions were used to generate a class of nonlocal reverse-spacetime integrable mKdV equations from the AKNS matrix spectral problems, leading to soliton solutions through solving corresponding generalized Riemann-Hilbert problems with the identity jump matrix.