Multiplicity of kink and hump structures in Van der Waals gas system

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.