Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions
Wen-Xiu Ma*
1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China 2Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia 3Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA 4School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa
Abstract：We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz–Kaup–Newell–Segur matrix eigenvalue problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding reflectionless Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and formulate their soliton solutions via those reflectionless Riemann–Hilbert problems. Soliton solutions are computed for three illustrative examples of scalar and two-component integrable fourth-order nonlinear Schrödinger equations.
Gesztesy F and Holden H 2003 Soliton Equations and Their Algebro-Geometric Solutions: (1+1)-Dimensional Continuous Models (Cambridge: Cambridge University Press)
2022, Vol. 39 
