title: Rogue waves of the Hirota and the Maxwell-Bloch equations.
abstract: In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch (H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fiber and further generalize it to the matrix form of the n-fold Darboux transformation of this system. This n-fold Darboux transformation implies the determinant representation of nth solutions of (E([n]),p([n]),η([n])) generated from the known solution of (E,p,η). The determinant representation of (E([n]),p([n]),η([n])) provides soliton solutions, positon solutions, and breather solutions (both bright and dark breathers) of the H-MB system. From the breather solutions, we also construct a bright and dark rogue wave solution for the H-MB system, which is currently one of the hottest topics in mathematics and physics. Surprisingly, the rogue wave solution for p and η has two peaks because of the order of the numerator and denominator of them. Meanwhile, after fixing the time and spatial parameters and changing two other unknown parameters α and β, we generate a rogue wave shape.
authors: Department of Mathematics, Ningbo University, Ningbo 315211, China.
authors: Chuanzhong
authors: C
authors: Li
authors: Jingsong
authors: J
authors: He
authors: K
authors: K
authors: Porsezian
authors: K
authors: K
authors: Porseizan
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical; D012212:Rheology / Q000379:methods*; D012542:Scattering, Radiation