Numerical Simulations of Coupled Solitary Waves With Spatially Modulated Non‐Linearity

This study investigates the dynamics of two coupled solitary waves propagating in media characterised by spatially modulated non‐linearity and variable dispersion. By employing numerical simulations of a system of coupled non‐linear Schrödinger equations (NLSEs) with varying coefficients, we analyse how inhomogeneous physical properties influence soliton stability and interaction. Our results demonstrate that spatial modulation of non‐linearity can control the velocity and amplitude of wave packets, providing a mechanism for soliton trapping or acceleration. Furthermore, we examine the role of the dispersion‐to‐non‐linearity ratio in maintaining the structural integrity of the coupled waves over long distances. These findings provide insights into optical signal processing in non‐uniform fibres and matter‐wave dynamics in Bose–Einstein condensates with varying trap potentials.