Computing the Dynamics of Optical Breathers in a Coupled Nonlinear Schrödinger Model with Dispersion Variations

In this work, we present a systematic and comprehensive analysis of vector breather dynamics in inhomogeneous optical media, modelled through a variable-coefficient coupled nonlinear Schrödinger (vc-CNLS) equation. This generalized model encompasses the fundamental components of Kerr-type nonlinear processes, including self-phase modulation, cross-phase modulation, and four-wave mixing, with temporally varying dispersion and nonlinear coefficients. Such variability effectively captures realistic physical settings where the optical properties of the medium evolve along the propagation direction or over time.

To explore the nonlinear wave dynamics supported by this framework, we construct explicit analytical breather solutions by employing a combination of similarity transformations and Darboux transformation techniques. This approach enables the generation of both Akhmediev breathers, which are localized in time and periodic in space, and Kuznetsov–Ma breathers, which display spatial localization and temporal periodicity. The resulting solutions reveal rich structures with controllable amplitudes, periods, and localization features. Our analysis demonstrates that the inhomogeneous nature of the medium plays a crucial role in shaping the evolution of optical breathers. In particular, variations in system parameters induce a diverse range of dynamical behaviors, including amplification, partial suppression, splitting, trapping, asymmetric deformation, and merging of oscillatory localized wave packets. These modulation effects highlight how engineered inhomogeneity can be used to tune or stabilize nonlinear excitations in practical optical systems. Overall, the findings contribute to a deeper understanding of localized coherent structures in variable nonlinear environments and offer potential pathways for controlling breather excitations in advanced optical communication, nonlinear photonic devices, and related applications.