Stability analysis, bifurcation analysis and exact solution of van der Waals form for the fluid granular matter

Articles in Press

Document Type : Research Paper

Authors

1 1. Reading College, Nanjing University of Information Science and Technology, 219 Ningliu, Nanjing 210044, P R China.\\ 2. Department of Mathematics, Dilla University, Dilla 419, Ethiopia.

2 Department of Electrical Engineering, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran.

3 Department of Mathematics, Northwest University, Kano, Nigeria.

4 Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran.

10.22034/cmde.2025.62567.2768

Abstract

This paper analyses one of the most popular models in nature and industry, the conventional type of van der Waals for granular fluids. The recognition of dynamic and static properties of such models is crucial in various areas of business, from engineering to pharmaceuticals and other physical phenomena, such as those explored in geophysics. The phase separation processis described in this model.This paper analyses one of the most popular models in nature and industry, the conventional type of van der Waals for granular fluids. The dynamic bifurcation methodis used to detect the existence of smooth and non-smooth dynamic bahaviours, and periodic, solitary, singular soliton, anti-kink, and kink wave profiles have been produced. As a result, the rich dynamic properties of the model help to utilize the extended direct algebra method to obtain exact wave solutions. Theachieved solutionswere compared with different approaches. As per the authors’ knowledge, no such work has yet been published in the literature.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 February 2026

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History

  • Receive Date: 19 July 2024
  • Revise Date: 17 December 2025
  • Accept Date: 15 January 2026

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