Nonlinear evolution equations in dispersive media: Analyzing the semilinear dispersive-fisher model

Abstract

The nonlinear Semilinear Dispersive-Fisher (SDF) model is an important equation describing wave dynamics in dispersive media influenced by nonlinear and diffusive effects. This study enhances both analytical and numerical methods to solve the SDF model and validate the solutions. We utilize the Modified Khater (MKhat) and Unified (UF) methods for analytical solutions, and He’s Variational Iteration (HVI) scheme for numerical approximations. Our investigation connects the SDF model to other nonlinear equations like the Korteweg–de Vries (KdV) and Fisher–Kolmogorov (FK) equations, demonstrating the consistency between analytical and numerical solutions. This research contributes to the understanding and modeling of wave phenomena in dispersive media with nonlinear and diffusive dynamics, offering refined analytical and numerical techniques specific to the SDF model. Key contributions include introducing the MKhat and UF methods for analytical solutions and employing the HVI scheme for numerical approximations, which are less represented in current literature. This work is positioned in mathematical physics, focusing on nonlinear evolution equations.