Investigating the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation: an iterative framework for nonlinear wave dynamics

This paper addresses the solution of the fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation using the Conformable Laplace Decomposition Method (CLDM). The CDGSK equation, a fundamental model in wave dynamics and fluid mechanics, is explored for its applications in quantum mechanics and nonlinear optics. By employing fractional calculus, we demonstrate how fractional derivatives influence the physical characteristics of wave propagation in both optical and quantum systems. The exact solutions obtained provide insight into soliton behavior, essential for understanding wave-particle interactions in quantum fields and light-matter interactions in optics. The fractional nature of the equation allows for more accurate modeling of non-integer order dynamics commonly found in optical fibers and quantum waveguides. The CLDM method proves to be highly effective, providing approximate solutions with minimal computational effort. These findings offer significant contributions to the fields of quantum mechanics and nonlinear optics, where the fractional CDGSK equation can be applied to solve complex wave equations with great accuracy.