Darboux transformation for a generalized Ablowitz-Kaup-Newell-Segur hierarchy equation

Abstract

A generalized Ablowitz-Kaup-Newell-Segur hierarchy of integrable equation from zero curvature equation is constructed based on the special orthogonal Lie algebra so(3, R), and the second equation is solved by the Darboux transformation. Besides, the soliton solutions are presented with the help of symbolic computation. Two special cases are given to make the solution more intuitive, and the dynamical properties of the solutions are discussed through the analysis of the graphics.