Investigating broadly dispersive solitons in optical couplers for metamaterials with nonlinear cubic-quintic-septic dynamics and white noise using distinct integration approaches

This study delves into the complex dynamics of stochastic coupled systems within an optical coupler designed explicitly for metamaterials operating under a cubic-quintic-septic nonlinearity. This system is characterized by its spatiotemporal dispersion and is subjected to the randomness introduced by multiplicative white noise. The primary objective of our investigation is to unravel the intricate behaviour of this system, which is crucial for advancing our understanding of nonlinear optical phenomena and for the development of innovative engineering solutions in the field of photonics. To achieve this, we employ three distinct analytical techniques: The unified Riccati expansion method, a refined version of Kudryashov's method, and a novel enhanced direct algebraic approach. An in-depth analysis of the impact of white noise on the soliton structures reveals significant fluctuations, offering new insights into the stability and dynamics of solitons in noisy environments.