fractional wave propagation in asymmetric nonlinear media: implications for metamaterial-based wave control

This study investigates the phenomenon of superarrival in gaussian wave packets propagating through a nonlinear fractional medium under the influence of a triangular potential barrier. the time-dependent fractional schrödinger equation is numerically solved using the split-step finite difference method to analyze the wave packet dynamics and transmission behavior in detail. the magnitude of superarrival is quantified and examined across a broad range of physical parameters, including the fractional order, nonlinearity strength, dispersion coefficient, wave packet width, initial velocity, and potential asymmetry. results reveal that superarrival is significantly enhanced in fractional and weakly nonlinear regimes and is highly sensitive to the degree of potential asymmetry. the observed behavior reflects the interplay between nonlocality and nonlinearity, characteristic of complex and engineered materials. these insights contribute to a deeper understanding of early arrival phenomena in wave dynamics and may provide theoretical support for controlling energy or information transport in next-generation devices. potential applications include quantum control, signal processing in photonic systems, and the design of metamaterials with tailored transmission properties at ultrafast or subwavelength scales.