Darboux dressing transformation and superregular breathers for a coupled nonlinear Schrödinger system with the negative coherent coupling in a weakly birefringent fibre

• Published in: International journal of computer mathematics Vol. 98; no. 12; pp. 2445 - 2460
• Main Authors: Tian, He-Yuan, Tian, Bo, Zhang, Chen-Rong, Chen, Su-Su
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.12.2021; Taylor & Francis Ltd
• Subjects: 35Q55 35B40 35Q60; Breathers; coupled nonlinear Schrödinger system with the negative coherent coupling; Coupling; Darboux dressing transformation; superregular breathers; Weakly birefringent fibre
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2021.1900568

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).