Darboux transformation and multi-dark soliton for N-component nonlinear Schrödinger equations

Abstract

In this paper, we obtain a uniform Darboux transformation for multi-component coupled nonlinear Schrödinger (NLS) equations, which can be reduced to all previously presented Darboux transformations. As a direct application, we derive the single dark soliton and multi-dark soliton solutions for multi-component NLS equations with a defocusing case and a mixed focusing and defocusing case. Some exact single and two-dark solitons of three-component NLS equations are investigated explicitly. The results are meaningful for vector dark soliton studies in many physical systems, such as Bose–Einstein condensate, nonlinear optics, etc.