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Tian, He-Yuan; Tian, Bo; Zhang, Chen-Rong; Chen, Su-Su

Darboux dressing transformation and superregular breathers for a coupled nonlinear Schrödinger system with the negative coherent coupling in a weakly birefringent fibre. (English) Zbl 1479.35827

Int. J. Comput. Math. 98, No. 12, 2445-2460 (2021).
Summary: 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).

Cited in 8 Documents

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
35Q60 PDEs in connection with optics and electromagnetic theory

Keywords:

weakly birefringent fibre; coupled nonlinear Schrödinger system with the negative coherent coupling; Darboux dressing transformation; superregular breathers
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References:

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