Binary Darboux transformations for a skew-symmetric matrix integrable nonlinear Schrödinger equation

The aim of this article is to construct a class of binary Darboux transformations for a skew-symmetric matrix integrable nonlinear Schrödinger equation. The associated AKNS-type Lax pairs, corresponding to the orthogonal Lie algebra so(2m), provide the framework necessary for systematically building these binary Darboux transformations. Direct, single-step applications of the transformations produce explicit soliton solutions. In particular, the M-matrix, central to the formulation of the binary Darboux transformations, is constructed within an extended framework that accommodates cases in which eigenvalues coincide with adjoint eigenvalues, thus incorporating the generalized Darboux transformations.