Darboux dressing transformation and superregular breathers for a coupled nonlinear Schrödinger system with the negative coherent coupling in a weakly birefringent fibre. Issue 12 (2nd December 2021)

• Record Type: Journal Article
• Authors: Tian, He-Yuan; Tian, Bo; Zhang, Chen-Rong; Chen, Su-Su
• Is Part Of: International journal of computer mathematics. Volume 98:Issue 12(2021)
• Page Start: 2445
• Page End: 2460
• Publication Date: 2021-12-02
• Subjects: Weakly birefringent fibre -- coupled nonlinear Schrödinger system with the negative coherent coupling -- Darboux dressing transformation -- superregular breathers; 35Q55 35B40 35Q60; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2021.1900568
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : For a coupled nonlinear Schrödinger system with the negative coherent coupling, which describes two orthogonally polarized pulses in a weakly birefringent fibre, we construct the Darboux dressing transformation and the N -th-order breather solutions with N as a positive integer. When the retarded time tends to be infinite, limits of the ratios between the N -th-order breather solutions and seed solutions are obtained. For the first-order breathers, we present the condition to distinguish the degenerate and nondegenerate cases. For the nondegenerate breathers, we analyse whether the breathers could be kink-type based on the above limits. For the second-order breathers, superregular breathers (SRBs) are derived, where each SRB could consist of two (1) kink-type, (2) single-hump or (3) double-hump quasi-Akhmediev breathers (quasi-ABs). Before and after the interaction, profiles of two quasi-ABs change for Case (1) but keep unchange for Case (2) or (3).