In this paper, we are going to solve nonlinear nonlocal reverse-time six-component six-order AKNS system. We used reverse-time reduction to reduce the coupled system to an integrable six-order NLS-type equation. Starting from the spectral problem of the AKNS system, a Riemann-Hilbert problem will be formulated. This formulation allows 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.
Long-time asymptotic behavior for the defocusing Hirota equation on a finite-genus algebro-geometric background
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；School of Mathematics and Information Science, Zhongyuan University of Technology（中原工学院数学与信息科学学院）
Inverse scattering transform and multiple high-order pole solutions for the nonlocal focusing and defocusing modified Korteweg-de Vries equation with the nonzero boundary conditions
Inverse scattering transform for the defocusing nonlinear Schrödinger equation with local and nonlocal nonlinearities under non-zero boundary conditions
On the global well-posedness for the nonlocal Fokas-Lenells equation with the weighted Sobolev initial data on the line
Zhongyuan University of Technology（中原工学院）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学学院国家重点实验室）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
