Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations

The coupled Maxwell–Bloch (CMB) system is a fundamental model describing the propagation of ultrashort laser pulses in a resonant medium with coherent three-level atomic transitions. In this paper, we consider an integrable generalization of the CMB equations with the defocusing case. The CMB hierarchy is derived with the aid of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>3</mml:mn> <mml:mo>×</mml:mo> <mml:mn>3</mml:mn> </mml:math> matrix eigenvalue problem and the Lenard recursion equation, from which the defocusing CMB model is proposed as a special reduction of the general CMB equations. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> -fold Darboux transformation as well as the multiparametric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> th-order rogue wave solution of the defocusing CMB equations are put forward in terms of Schur polynomials. As an application, the explicit rogue wave solutions from first to second order are presented. Apart from the traditional dark rogue wave, bright rogue wave and four-petalled rogue wave, some novel rogue wave structures such as the dark four-peaked rogue wave and the double-ridged rogue wave are found. Moreover, the second-order rogue wave triplets which contain a fixed number of these rogue waves are shown.