The dynamical structures of the Sharma–Tasso–Olver model in doubly dispersive medium

Abstract

In this article, the Sharma–Tasso–Olver model is investigated which characterizes the nonlinear double-dispersive evolution dispersive waves’ dynamical propagation in heterogeneous mediums. To study the dynamical nature of moving waves with a periodic and isolated nature analytically, the governing model is converted into an ordinary differential equation via a wave transformation to employ the extended modified auxiliary equation mapping approach and the G′G2 expansion method. In order to validate the computations, the stability of the obtained results is also established. It has been found that the model supports nonlinear solitary waves, periodic waves, shock waves and stable oscillatory waves. For a set of appropriate parameters, Mathematica is used to represent the dynamics of various wave structures as 3D, 2D and contour visualizations. Additionally, we may remark that the results discussed here are novel and innovative.