A binary Darboux transformation for multi-component nonlinear Schrödinger equations and dark vector soliton solutions

Abstract

By taking the plane wave potentials as the seed solutions, we harness a binary Darboux transformation to generate dark vector soliton solutions for multi-component nonlinear Schrödinger equations. We introduce a generalized Darboux matrix such that the eigenvalues could equal the adjoint eigenvalues. The method which is purely algebraic could be useful and convenient, particularly in the construction of dark soliton solutions of integrable systems.