Mathematical Modeling and Simulation of Nonlinear Wave Propagation in Complex Media

Abstract

Nonlinear wave propagation in complex media This has become an important field of research in applied mathematics, computational physics, and engineering as a result of its many applications in optical communication, seismic analysis, plasma physics, biomedical acoustics and electromagnetic systems.Nevertheless, modelling the nonlinear wave behaviour in non-homogeneous and non-dispersive media is still a central problem due to the inability of traditional linear models to model nonlinear interactions, dispersion and dissipation effects, and irregularities of the medium.This paper seeks to work out a strong mathematical and computational model of nonlinear wave propagation in complex media with nonlinear partial differential equations that employ state-of-the-art numerical simulation models.The proposed model will use nonlinear terms of interaction, damping properties and medium properties which vary spatially to reflect the realistic propagation environments.Numerical solution of the governing equations is provided by a discretization method that is based on the finite difference method and time is discretized with stability-controlled time integration to provide computational accuracy and convergence.The simulations indicate the development of nonlinear waves (steepening of waves, modulation of amplitudes, deformation caused by dispersion, and localized energy concentration) in different medium conditions and using nonlinear coefficients.The results also show that the proposed framework is numerically more stable and predictive than the traditional linear propagation models.The methodology developed provides great potential in practical applications to the next-generation communication systems, geophysical exploration, acoustic imaging, and advanced computational wave engineering as well as contributes to a greater body of knowledge on nonlinear dynamical behavior of complex physical systems.