Generation and manipulation of rogue waves in an erbium-doped fiber under variable pulse width and gain(loss) effects

We report an analysis on the control of nonautonomous rogue waves (RWs) in inhomogeneous erbium-doped optical fibers with variable pulse widths. The analysis is carried out within the framework of the variable-coefficient coupled nonlinear Schrödinger–Maxwell–Bloch (vc-NLSMB) equation, incorporating variable dispersion, nonlinearity, gain(loss), and inhomogeneous broadening terms. Using a multivariate similarity transformation, we formulate first-, second-, and third-order RW solutions of the vc-NLSMB equation. The impact of different gain(loss) distributions, dispersion, and nonlinearity parameters on these solutions are systematically explored. In the absence of gain or loss, the rogue waves exhibit Kuznetsov–Ma breather-like characteristics due to periodic modulation of the dispersion coefficient. For nonzero gain(loss) values, however, the rogue waves evolve on controllable backgrounds that are bell-shaped, periodic, or hump-like, corresponding to hyperbolic, periodic, and linear gain(loss) profiles, respectively. The inhomogeneous broadening term further modifies the background structure in each case. These findings offer new aspects into the controllable rogue wave dynamics in inhomogeneous nonlinear optical systems.