INVESTIGATION OF SOLITARY AND KINK WAVE SOLUTIONS FOR THE CONFORMABLE CONCATENATION MODEL WITH SPATIO–TEMPORAL DISPERSION AND CHROMATIC DISPERSION

This work investigates solitary and kink wave solutions of a conformable fractional concatenation model that includes spatio-temporal dispersion (STD) and chromatic dispersion (CD). It employs two distinct analytical techniques: the modified auxiliary equation approach and the [Formula: see text]-expansion method, to develop new exact solutions for traveling waves. It further studies the bifurcation structure of the reduced system to explain the existence of solitary and kink wave solutions for the governing model. Numerical simulations also show how the fractional derivative order and dispersion parameters affect the solutions that were found. Compared to previous studies that solely examined classical models, this study provides a novel conformable fractional analysis, which increases its use in wave propagation and nonlinear optics. Moreover, the findings contribute to our understanding of wave events in fractional models and provide intriguing directions for further research and point to interesting areas for further investigation.