Implicit quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion and power–law of self–phase modulation by Lie symmetry

The focus of this paper lies in uncovering implicit quiescent optical solitons within a concatenation model. This model is characterized by nonlinear chromatic dispersion and a power-law representation of self-phase modulation. To achieve this, we employ a mathematical technique known as Lie symmetry analysis. This analytical tool proves crucial in successfully identifying and revealing these soliton structures within the concatenation model. Through the application of Lie symmetry analysis, we gain a profound understanding of the system’s temporal dynamics. This encompasses both the linear temporal evolution and a more generalized version of temporal evolution. The investigation into linear temporal evolution provides insights into the fundamental behavior of the system, while the exploration of generalized temporal evolution uncovers more intricate and nuanced aspects of the soliton behavior.