Interactions of soliton solutions for the generalized viscous capillarity compressible fluid model

In this work, interactions in a generalized viscous capillarity compressible fluid model are studied analytically employing the approach of Hirota bilinear transformation. We examine the conservation laws of the p-system with a generalized cubic van der Waals flow, nonlinear viscosity, and capillarity factors. This approach is used in the study to show numerous novel wave shapes and solitary solutions in compressible isothermal viscosity-capillarity van der Waals fluids. With the help of Mathematica, we extract various wave phenomena such as bright and dark breathers, kink, anti-kink, periodic lumps, periodic cross kink, M-shaped, mixed and multiple wave structures. The 3D dynamical behaviours and their related contour profiles for the obtained solutions are presented. The Hirota bilinear transformation approach's effectiveness and clarity, as shown in this paper, underscore its potential as a useful tool for deciphering complex physical processes.