Exact solution classification and physical interpretation for the concatenation model with Kerr law nonlinearity via trial equation method and complete discrimination system for polynomials method

The Concatenation model with Kerr law nonlinearity integrates three typical nonlinear optical equations to describe the complex Kerr nonlinear effects of ultrashort pulse propagation in optical fibers. This study employed the trial equation method combined with the complete discrimination system for polynomials method to solve the model and derive its exact solutions. Multiple types of solutions were obtained, including solitary wave, Jacobi elliptic function, and trigonometric function solutions. Corresponding two-dimensional and three-dimensional visualizations were plotted to intuitively demonstrate the physical features of these solutions. The findings provide valuable theoretical support for the analysis of ultrashort pulse transmission and the application of nonlinear optical systems.