Perturbation of Highly Dispersive Solitons in Optical Metamaterials with Twin-Core Couplers and Power-Law of Self-Phase Modulation by Laplace–Adomian Decomposition

This paper utilizes the Laplace–Adomian decomposition method to numerically investigate the highly dispersive bright soliton solutions in twin-core optical couplers that employ metamaterials as waveguides. The focus of the study is on the power-law self-phase modulation. The results of the simulations and the accompanying error analysis demonstrate exceptional accuracy for this numerical approach. These findings suggest that the Laplace–Adomian decomposition method is a robust tool for tackling complex nonlinear problems in optical systems. Furthermore, the implications of this research could pave the way for advancements in the design and optimization of metamaterial-based waveguides, potentially leading to improved performance in applications, such as telecommunications and sensing technologies.