Fractional Optical Solitons in Metamaterial-Based Couplers with Strong Dispersion and Parabolic Nonlinearity

The current study examines optical soliton solutions in a complicated system of metamaterial-based optical solutions coupled with extremely dispersive couplers. The conformable fractional derivative (CFD) influences the nonlinear refractive index, which is governed by a parabolic equation. Some soliton solutions are extracted, like bright, singular solitons, and singular periodic ones; also, Weierstrass elliptic doubly periodic, and several other exact solutions are systematically revealed by the study using the modified extended direct algebraic method. The findings shed important light on the many solitons in these intricate systems and the interactions between nonlinearity, dispersion, and metamaterial properties. The findings have significance beyond advancing our theoretical understanding of soliton behavior in metamaterial-based optical couplers; they might influence the advancement and development of optical communication technologies and systems. Complementary 2D and 3D representations show how stability parameters change throughout various dynamical regimes and confirm solution consistency. In order to comprehend the complex nonlinear phenomena of this system and its possible practical applications, this paper offers a comprehensive theoretical framework.