Dynamical analysis and numerous signal transmission behavior of the nonlinear Pochhammer-Chree (PC) model via two consistent schemes

This investigation conducts a comprehensive analytical analysis of the renowned nonlinear Pochhammer-Chree (PC) model by utilizing two efficient methods. The nonlinear PC model stands as a robust tool for the analysis of movement of traveling waves in a substantially long cylindrical rod with a circular cross-section, and longitudinal wave such as sound and particle wave propagation through elastic medium. The PC model also plays very important role in explaining various natural and engineering applications. To establish these results, we employ the generalized exponential rational function (GERF) method and the auxiliary equation (AE) method. The obtain results uncover numerous secrete dynamical characteristics of the model. Here, we also examine the influences of wave propagation velocity parameter on the attained solutions to understand the inner mechanism and dynamical signal transmission behavior of the related phenomenon. The gestures of obtained results are explained by representing the 3-dimensional (3D) and 2-dimensional (2D) shapes. The attained solutions demonstrate that the employed techniques are straightforward, reliable, functional and more effective to extracting soliton solutions of numerous nonlinear models.