Optical solitons for the concatenation model with power–law of self–phase modulation by lie symmetry

This paper investigates the concatenation model under the influence of power-law self-phase modulation through the Lie symmetry. We employ two integration schemes, namely the extended tanh approach and the F-expansion algorithm, to rigorously integrate the reduced ordinary differential equations governing the system. Through this methodological framework, we uncover a diverse array of soliton solutions and systematically classify them, shedding light on their intricate dynamics and characteristics. Our research unveils previously undiscovered soliton solutions, enriching the existing understanding of concatenation models. We introduce a comprehensive classification scheme for these solitons, providing valuable insights into their behavior and interactions. Numerical simulations validate the stability and persistence of the identified soliton solutions across various parameter regimes. Our findings contribute to the theoretical framework of nonlinear wave dynamics and hold potential for innovative applications in fields such as nonlinear optics and information processing.