Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled Hirota–Maxwell–Bloch equations

Abstract

We propose the system of generalized inhomogeneous coupled Hirota–Maxwell–Bloch equations which describes propagation of an optical soliton in an inhomogeneous erbium-doped fiber with two-level resonant atoms. For this system, higher-order dispersion, self-steepening and self-Raman scattering are assumed to be inhomogeneous, like the group velocity dispersion. The exact analytical multisoliton solutions are obtained by employing the simple, straightforward Darboux transformation based on the obtained 3 × 3 Lax pair. As an example, the one- and two-soliton solutions in explicit forms are generated. Then, we give the relative numerical evolution and discuss the propagation characteristics of the pulse.

New types of exact quasi-soliton solutions in metamaterials

“…So far, theoretical models for ultrashort pulse propagation in MMs have been established [17][18][19][20]. Some authors have investigated the modulation instability in MMs closely associated with the existence of solitons or solitary waves [21][22][23]. Bright and dark solitons, combined solitary waves and periodic waves have been analytically or numerically studied from different viewpoints [24][25][26][27][28][29][30][31][32].…”

Publisher's Note:N-order bright and dark rogue waves in a resonant erbium-doped fiber system [Phys. Rev. E86, 066603 (2012)]

“…Recently, considering all higher order effects in the propagation of femtosecond pulses, the coupled Hirota and Maxwell-Bloch (CH-MB) equations have been proposed and analyzed for soliton solutions [12]. Some generalization of NLS-MB equations, for instance, the CH-MB equations and the NLS-MB equations with variable dispersion and nonlinear effects are discussed [13][14][15]. The single soliton and the single breather solutions [16] of the NLS-MB equations are given by the Darboux transformation (DT) [17,18].…”

N-order bright and dark rogue waves in a resonant erbium-doped fiber system

“…Recently, considering all higher order effects in the propagation of femtosecond pulses, the coupled Hirota and Maxwell-Bloch (CH-MB) equations have been proposed and analyzed for soliton solutions [12]. Some generalization of NLS-MB equations, for instance, the CH-MB equations and the NLS-MB equations with variable dispersion and nonlinear effects are discussed [13][14][15]. The single soliton and the single breather solutions [16] of the NLS-MB equations are given by the Darboux transformation (DT) [17,18].…”