@article{Ali2025, 
author = {Rashid Ali and Rabia Imtiaz and Moin-ud-Din Junjua and Fuad A. Awwad and Emad A. A. Ismail and Ahmed S. Hendy},
title = {Multiplicity of kink and hump structures in Van der Waals gas system},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {5},
pages = {12493-12518},
keywords = {Van der Waals gas system, nonlinear partial differential equation, Riccati modified extended simple equation method, kink and hump solitons, Riccati equation},
url = {https://www.sciopen.com/article/10.3934/math.2025564},
doi = {10.3934/math.2025564},
abstract = {In this work, numerous features of the nonlinear Van der Waals gas system in the sense of viscosity capillarity are analytically and theoretically investigated. A novel trustworthy integrating approach, namely the Riccati modified extended simple equation method (RMESEM), is utilized to determine the physical nature of the system. This technique successfully generates a novel range of kink, anti-kink, cuspon kink, and bell-shaped bright and dark hump solitary wave solutions in the form of exponential, periodic, hyperbolic, rational, and rational-hyperbolic functions. Using suitable parameter values that satisfy constraint criteria, we generate a set of 2D graphs to improve comprehension and graphically depict these solitary wave solutions. The efficiency and adaptability of our method in solving a range of nonlinear problems in mathematical science and engineering are validated by our computational research.}
}