Higher-order Optical Rogue Waves in Spatially Inhomogeneous Multimode Fiber

The objective is to explore the mathematical analysis to understand and manipulate the dynamics of higher-order rogue waves in an inhomogeneous multi-mode optical media. For this purpose, we consider a theoretical model represented by the coupled nonlinear Schrödinger equations consisting of the spatially varying dispersion and nonlinearities arising from both coherent and incoherent nonlinear effects, which drives the spatially modulated linear and nonlinear refractive index of the media. We construct controllable spatiotemporally (doubly) localized rogue wave solutions through Darboux transformation and by designing a similarity transformation. Explicitly, we investigate the evolution of first- and second-order vector rogue waves possessing different characteristics such as degenerate and non-degenerate type bright, gray, and dark localized profiles that can be controlled by the inhomogeneity arising in the medium and polarization parameters available in the solutions. To highlight the consequences of the spatially inhomogeneous nature of the medium, we demonstrate the transition mechanism of rogue waves by adopting four different spatial modulations, namely periodic, hyperbolic, and localized behavior, by incorporating Jacobi elliptic functions. Significantly, these modulations lead to the transition of rogue waves to spatially-periodic Akhmediev breathers of single- and multi-peak symmetric and asymmetric behavior arising on top of snoidal, cnoidal, and dnoidal backgrounds. Further, the rogue waves experience amplification, suppression, splitting, and trapping due to localized soliton type background modulations. The observed results will facilitate improvement in understanding other types of localized nonlinear waves in different inhomogeneous media.