Darboux transformations and solutions of nonlocal Hirota and Maxwell-Bloch equations

Abstract

In this paper, based on the Hirota and Maxwell-Bloch (H-MB) system and its application in the theory of the femtosecond pulse propagation through an erbium doped fiber, we define two kinds of nonlocal Hirota and Maxwell-Bloch (NH-MB) systems, namely, $PT$-symmetric NH-MB system and reverse space-time NH-MB system. Then we construct the Darboux transformations of these NH-MB systems. Meanwhile, we derive the explicit solutions by the Darboux transformations.

arXiv comment22 Pages, accepted for publication in Studies in Applied Mathematics

References in corpus (7)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Integrable nonlocal Hirota equations
• Category of nonlinear evolution equations, algebraic structure, and r-matrix
• Nonstandard bilinearization of $\mathcal{P}\mathcal{T}$-invariant nonlocal nonlinear Schrödinger equation: Bright soliton solutions
• Localized excitations and interactional solutions for the reduced Maxwell-Bloch equations
• On symmetry preserving and symmetry broken bright, dark and antidark soliton solutions of nonlocal nonlinear Schrödinger equation
• Inverse scattering transform for two-level systems with nonzero background