Effect of quartic nonlinearity on elastic waves via successive approximation

The theory of nonlinear elastic wave propagation is important in multiple scientific and engineering fields. In this study, we present a comprehensive examination of nonlinear elastic wave profiles through a contemporary approach of successive approximation. This research is related to nonlinear elastic wave models along different types of nonlinearities. Murnaghan potential is used due to the assumption of the hyper-elastic materials. We explore the complication of the governing equations and go through the behaviors of nonlinear waves in one dimension. The comparative aspect of our study is a distinctive feature, as we evaluate and contrast the results obtained using successive approximation along different nonlinearities. Additionally, we present graphical representations of our findings, enhancing the visual comprehension of the wave profiles and their evolution. This study contributes to the nonlinear elastic wave analysis and comparison.