Analysis of Solitary-Wave Structures in Gases Governed by the Generalized Van Der Waals Equation via the Improved G′/G-Expansion Method

The generalized van der Waals equation shows an influential role in studying nonlinear wave propagation phenomena in gas dynamics and fluidized granular media. On the other hand, the complexity of the associated nonlinear partial differential equation makes the problem of finding the exact solution of the nonlinear model and analyzing its behavior highly challenging. This study considers the improved G′/G-expansion technique to obtain the travelling wave solution for the generalized van der Waals equation. In fact, the introduced method simplifies the nonlinear equation to the ordinary differential equation, which gives various kinds of analytical solutions such as trigonometric, hyperbolic, and rational functions. For certain values of parameters, the obtained solutions take many kinds of solitary waves. In addition, graphical simulation techniques are employed to illuminate the physical characteristics of the attained wave solutions. The results obtained provide new perspectives on the analysis of nonlinear waves in gas dynamics and fluidized granular systems governed by the generalized van der Waals equation of state. The novelty of this paper is the combination of exact traveling-wave generation with the planar dynamical study of the generalized van der Waals system, as well as the investigation of perturbation-induced transitions to quasiperiodic and chaotic regimes.