The formation of optical soliton solutions of the Kudryashov equation using the unified auxiliary equation method

In this work, we examine the dynamic properties of the well-known Kudryashov equation in the context of pulse propagation within optical fibers. For this purpose, we utilize the unified auxiliary equation method (UAEM), which is a powerful technique for deriving abundant exact solutions for nonlinear partial differential equations. Using a suitable wave transformation changes the given equation is converted into an ordinary differential equation, which makes it possible to treat it systematically. Through an extensive list of Jacobi elliptic functions in the UAEM, a large number of exact solutions are created, comprising singular, kink, dark, bright, rational, and combined solutions. Soliton theory is especially significant because solitons are stable, localized nonlinear waves that preserve their shape and energy during propagation and interaction. Due to this property, they are essential for comprehending nonlinear wave dynamics as well as for real-world uses like fluid dynamics, plasma waves, and long-distance optical communication.