Exact optical soliton solutions and interaction dynamics in fractional nonlinear systems

This paper aims to provide a rigorous analytical investigation of multisoliton dynamics within a conformable concatenated nonlinear framework that unifies the nonlinear Schrödinger, Sasa Satsuma, and Lakshmanan Porsezian Daniel equations through the incorporation of a conformable fractional derivative. By extending classical calculus to encompass fractional-order dynamics, the model captures intricate higher-order dispersion and non-linear interactions that critically influence pulse propagation in optical fibers. Employing advanced techniques such as the modified simplest equation method and the Kudryashov method, we derive a comprehensive family of exact soliton solutions including bright, dark, and mixed profiles and establish explicit parameter relations governing their stability and evolution. Detailed numerical simulations further elucidate the effects of the fractional parameter on soliton propagation, interaction dynamics, and energy conservation.