Breather interactions and higher-order nonautonomous rogue waves for the inhomogeneous nonlinear Schrödinger Maxwell–Bloch equations

• Published in: Annals of physics 2015-08, Vol.359, p.97-114
• Main Authors: Wang, Lei, Li, Xiao, Qi, Feng-Hua, Zhang, Lu-Lu
• Format: Article
• Language: English
• Subjects: [formula omitted]-fold variable-coefficient modified Darboux transformation; Breather interaction; Higher-order nonautonomous rogue wave; Inhomogeneous nonlinear Schrödinger Maxwell–Bloch equation; Nonlinear equations; Physics; Wave power
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2015.04.025

Under investigation in this paper are the inhomogeneous nonlinear Schrödinger Maxwell–Bloch (INLS-MB) equations which model the propagation of optical waves in an inhomogeneous nonlinear light guide doped with two-level resonant atoms. Higher-order nonautonomous breather as well as rogue wave solutions in terms of the determinants for the INLS-MB equations are presented via the n-fold variable-coefficient modified Darboux transformation. The interactions among two nonautonomous breathers are graphically discussed, including the fundamental breather, bound breather, two-breather compression and two-breather evolution, etc. Moreover, several patterns of the higher-order rogue waves are also exhibited, such as the square rogue wave, two- and three-order periodic rogue waves, periodic fission and fusion, two-order stationary rogue waves, and recurrence of the two-order rogue waves. The character of the trajectory of the two-order periodic rogue wave is analyzed. Additionally, a novel type of interaction, namely, the collision between the breather and long-lived rogue waves, is found to be elastic. Our results could be useful for controlling the nonautonomous optical breathers and rogue waves in the inhomogeneous erbium doped fiber.