Novel highly dispersive soliton solutions in couplers for optical metamaterials: leveraging generalized Kudryashov’s Law of refractive index with eighth-order dispersion and multiplicative white noise

Abstract This article represents a significant advancement in the understanding of highly dispersive optical solitons within the context of optical metamaterials, leveraging a generalized form of Kudryashov’s law of refractive index. By integrating eighth-order dispersion and multiplicative white noise into the analysis, crucial elements in the development and optimization of sophisticated optical metamaterials are accounted for in this current paper for the first time. Through an improved direct algebraic method, a diverse range of soliton solutions are derived, encompassing bright, dark, singular, and straddled solitons. Moreover, the study goes beyond mere derivation by presenting exact solutions expressed using Jacobi and Weierstrass’s elliptic functions. This mathematical framework offers deeper insights into the dynamics of solitons within the investigated context. These findings substantially expand the theoretical underpinnings governing optical solitons in metamaterials, with direct implications for the design, and implementation of next-generation optical devices. The bridging of theoretical advancements with practical applications underscores the significance of this work. By elucidating precise control over soliton properties, it lays the groundwork for innovative solutions in optical communications and beyond. Also, this research serves as a crucial stepping stone towards realizing the full potential of optical metamaterials in shaping the future of optical technologies.