Riemann–Hilbert problems of a nonlocal reverse-time AKNS system of six-order and dynamical behaviors of N-soliton

Abstract

In this paper, we solve nonlinear nonlocal reverse-time six-component sixth-order AKNS system. We used reverse-time reduction to reduce the coupled system to an integrable sixth-order nonlinear Schrödinger-type equation. Starting from the spectral problem of the AKNS system, a Riemann–Hilbert problem will be formulated. This formulation allows us to generate soliton solutions by using the vectors lying in the kernel of the matrix Jost solutions. When reflection coefficients are zeros, the jump matrix is identity and the corresponding Riemann–Hilbert problem yields soliton solutions, leading to explore their dynamics.