High-order optical rogue waves in two coherently coupled nonlinear Schrödinger equations

Abstract

In this paper, starting from the matrix nonlinear Schrödinger equation that describes Bose–Einstein condensation, we derive two coherently coupled nonlinear Schrödinger equations via two distinct reductions. Subsequently, we construct the $N$-fold generalized Darboux transformation to investigate the high-order rogue wave solutions of the two equations based on their non-zero seed solutions. Furthermore, the dynamical behaviors of these exact rogue wave solutions are explicitly described graphically. Unlike the well-known eye-shaped and four-petaled rogue waves observed in Manakov equation, some novel behaviors of nonlinear dynamics in these coherently coupled systems are discovered. Additionally, we investigate the asymptotic behavior of the second-order rogue wave solutions and the mixed interaction structures. The findings of this work will contribute to the investigation of optical rogue waves in optical fibers with coherent effects.