Book Title: Innovative Approaches in Multidisciplinary Research and Development (IAMRD)
Chief Editors: Dr. Anil Kashinath Salunke and Dr. Rituraj Pant
Associate Editors: Prof. (Dr.) Sourav Madhur Dey and Dr. Amrutha Satheesan
Co-Editors: Dr. Souvik Sur and Dr. Phakir Singh
ISBN: 978-93-7183-004-1
Chapter: 15
DOI: https://doi.org/10.59646/708/15
Author: Dr. Santosh Govindrao Bodkhe
Abstract
Nonlinear wave propagation in inhomogeneous media is important for many physical systems such as in geophysical structures, optical materials and plasma environments. In this research paper, the propagation of nonlinear waves in media with spatial variations in their parameters is studied from the perspective of the influence of inhomogeneities on the wave speed, amplitude modulation, dispersion and redistribution of the energy of the wave. The study is based on a combination of a theoretical and computational approach, where nonlinear wave equations and medium-variation models are applied to study the propagation characteristics under different conditions. The results show that the inhomogeneity has a significant influence on the dynamics of the waves, causing phenomena like wave distortion and localized concentration of energy, as well as nonlinear scattering effects. For strongly inhomogeneous media, there is reduced stability of the waves, and the interactions of the nonlinearity and spatial variation lead to complex propagation patterns that are not predictable. But under controlled conditions, these effects can be used as a guide to waves, improve the signal strength, and focus energy. Additionally, the analysis reveals that the influence of the medium variations on the wave behavior is enhanced by the presence of nonlinear effects and the accurate modelling of the wave behavior is fundamental to perform predictive analysis. The paper also suggests some applications in seismic imaging, optical fiber communication and electromagnetic wave control. The study results highlight the delicate balance between the nonlinearity of the waves and the material structure in nonlinear wave propagation in inhomogeneous media, and indicate both challenges and opportunities for new scientific and engineering applications. The present work builds upon the current understanding of the effects of spatial inhomogeneity on the evolution of nonlinear waves and summarizes future directions of research in systems of complex media. In addition, numerical simulation is shown to agree with experimental measurements, and it is found that a small change in the medium properties can cause large changes in the trajectory and intensity distribution of the waves. The results also indicate that the use of higher-order nonlinear terms may enhance the accuracy of the predictive wave models in complex environments.
Keywords: Nonlinear waves; Inhomogeneous media; Wave propagation; Nonlinear dynamics; Dispersion; Wave scattering; Spatial variability; Wave modelling; Geophysical waves; Optical physics.