Exact solutions and applications of inhomogeneous vector solitons in optical media

Traditional models of soliton dynamics often rely on single-mode approximations; however, practical optical fibers typically exhibit structural inhomogeneities and birefringence, resulting in complex multi-mode interactions. To better capture these dynamics, the scalar nonlinear Schrödinger equation (NLSE) has been extended to vector coupled NLSEs (CNLSEs), which offer a more realistic framework for describing pulse propagation in such environments. In this work, we study the evolution of vector solitons in inhomogeneous two-mode optical fibers governed by a generalized system of coupled NLSEs with ten variable coefficients–significantly generalizing prior models limited to five. Our formulation incorporates key physical effects, including variable group velocity dispersion, self- and cross-phase modulation, linear gain or loss, and external electro-optic phase modulation. Using a similarity transformation method, we reduce the variable-coefficient system to its constant-coefficient counterpart and derive exact analytical solutions. A distinguishing feature of our approach is the classification of self-similar dynamics into two distinct regimes: one with an internal quadratic potential allowing arbitrary scaling functions, and one with a vanishing potential where the pulse shape is determined by compatibility constraints. This classification leads to the construction of nine families of novel chirped similariton solutions, including W-shaped-dipole, bright-dipole, dark-dipoles, and kink-anti-kink-dipole. Numerical simulations confirm that strongly chirped similaritons exhibit greater robustness and structural stability, whereas their weakly chirped counterparts may display breather-like oscillations. These results demonstrate the tunability of soliton characteristics via system parameters and highlight the potential of the model for applications in nonlinear photonics, ultrafast optical signal processing, and Bose–Einstein condensates.