Higher-order vector rogue waves in inhomogeneous optical media: insights into variable-coefficient coupled nonlinear schrödinger model with four-wave mixing
摘要
The present work focuses on a systematic analysis of higher-order vector rogue wave dynamics in inhomogeneous optical media, which we execute by exploring a variable-coefficient general coupled nonlinear Schrödinger model with four-wave mixing effects. We construct explicit higher-order rogue wave solutions through a new type of nontrivial three-layer methodology involving a linear superposition formula, generalized similarity, and Darboux transformations. The obtained solution exhibits bright, dark, and gray-type spatiotemporally localized structures, revealing diverse patterns on constant and periodic backgrounds. Based on the exhibiting patterns, we classify the obtained rogue waves into singlet, doublet, triplet, quartet, and sextet rogue patterns, admitting dot, line, triangular, rhombus, and pentagon structures. Importantly, the inhomogeneity that arises in the medium modulates the characteristics of the rogue waves, demonstrating various phenomena such as partial suppression, amplification, splitting, trapping, and merger of localized peaks with asymmetric deformation and collapse into the background. The findings of the present work can encourage a more profound understanding of rogue waves and other localized coherent structures across diverse inhomogeneous media.