Darboux transformation and multi-dark soliton for N-component nonlinear Schrödinger equations. (5th August 2015)

• Record Type: Journal Article
• Authors: Ling, Liming; Zhao, Li-Chen; Guo, Boling
• Is Part Of: Nonlinearity. Volume 28:Number 9(2015:Sep.)
• Page Start: 3243
• Page End: 3261
• Publication Date: 2015-08-05
• Subjects: Darboux transformation -- dark soliton -- N-component NLS equations; 37K15 -- 37K35 -- 35C08; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/9/3243
• Languages: English
• ISSNs: 0951-7715

Abstract

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.