Dynamic Solitary Wave Solutions Arising in Nonlinear Chains of Atoms Model

This article consists of several travelling wave soliton solutions for solving a complex nonlinear chains of atoms model with long-range interactions via the generalized auxiliary equation method. We have converted considered PDE into nonlinear ODE by utilizing the specific wave transformation. The solutions attained in the form of periodic, bright, singular, W and M types. The adapted method seems a very impressive and competent avenue to obtain the exact soliton solutions of several advanced distinct models. Moreover, to understand the physical nature of the newly attained solutions 2D, 3D and contour-type graphs are presented with distinct dimensions. Additionally, sensitivity and stability through a dynamical system and with the use of different initial conditions are successfully analyzed.