The dynamic behavior of Van der Waals gas system based on new extended (G'/G)-expansion method

In this study, I theoretically explored different aspects of the (1+1)-dimensional Van der Waals (VDW) gas system in the viscosity capillarity sense. To find the physical nature of the described system, a couple of new reliable integrating techniques such as the extended (N, R) expansion method and the new extended (G'/G)-expansion method were used, and a variety of soliton solutions were successfully derived. To enhance our understanding and visually represent these solutions, I created 2D and 3D plots, thereby utilizing appropriate parameter values that met the constraint conditions. Furthermore, I analyzed chaotic behavior, thereby observing its presence in the perturbed dynamical system and obtaining positive results that support chaotic motion. My computational analysis confirmed the effectiveness and versatility of my techniques in addressing nonlinear problems in mathematical science and engineering.