Nonlinear wave dynamics and soliton solutions of the Rosenau equation with conformable fractional derivatives

The nonlinear partial differential equations considered in this study are important in modeling complex wave phenomena extending from hydrodynamics via ocean engineering to plasma physics, fluid dynamics, and other mediums. The Rosenau equation provides an analytical solution for studying wave phenomena in many physical systems, where dispersion and nonlinear dynamics play significant roles. This equation is proposed to explain the dense dynamic behavior of discrete systems. The generalized exponential rational function method has been employed to obtain the new soliton solutions of a nonlinear wave equation in fluid dynamics. This work uses the conformal fractional derivative and the fractional wave transformation to get the analytical results. The solutions include trigonometric, hyperbolic, and exponential functions with possible representations into three-dimensional graphics showing wave dynamics. The study focuses on the nonlinear Rosenau equation, revealing wave features including dark and bright solitons, and kinks and anti-kink waves. We are examining how parameters may have their impact on stability and interactions. This work enhances our knowledge of nonlinear wave systems and their practical applications in fluid dynamics and materials science.