The three-level coupled Maxwell-Bloch equations: rogue waves, semirational rogue waves and W-shaped solitons
arXiv:2002.04174
Abstract
In this paper the coupled Maxwell-Bloch equations which describe the propagation of two optical pulses in an optical medium with coherent three-level atoms are studied by Darboux transformation. The general nth-order rogue wave solution involving two different choices of multiple roots for the spectral characteristic equation and the multiparametric nth-order semirational solution are both obtained in terms of Schur polynomials. The explicit rogue wave solutions and semirational solutions from first to second order are provided. In contrast to the known Peregrine soliton, dark and four-petaled structures, some unusual patterns such as triple-hole, twisted-pair, composite four-petaled and composite dark rogue waves are put forward. Moreover, the interaction between dark-bright soliton and dark rogue wave and interaction between breather and dark rogue wave are shown. Further, the higher-order nonlinear superposition modes which feature triple and quadruple temporal-spatial distributions are presented. Finally, the state transition between rogue wave and W-shaped soliton is found where the modulation instability growth rate tends to zero under the low perturbation frequency. Particularly, the dark and double-peak W-shaped solitons are examined.
arXiv comment22 pages, 9 figures
References in corpus (13)
- Deterministic Vector Freak Waves
- Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
- A generating mechanism for higher order rogue waves
- Rogue waves in the Davey-Stewartson equation
- Rogue waves emerging from the resonant interaction of three waves
- High-order Rogue Waves in Vector Nonlinear Schrödinger Equations
- State Transition Induced by Higher-order Effects and Background Frequency
- Trajectory Characters of Rogue Waves
- Periodic and rational solutions of the reduced Maxwell-Bloch equations
- Matched Pulse Propagation in a Three-Level System
- Different types of nonlinear localized and periodic waves in an erbium-doped fiber system
- High-order rogue waves of a long wave-short wave model
- Rogue wave triggered at a critical frequency of a nonlinear resonant medium