Novel topological, non-topological, and more solitons of the generalized cubic p-system describing isothermal flux

In fluid dynamics, mixed-type systems of conservation laws model a wide range of phase transition problems in compressible media. This analysis studies analytically the time-fractional mixed-type hyperbolic-elliptic van der Waals p-system with generalized cubic flux function for the first time. For this purpose, the expanded ansatz method is introduced and employed to derive new closed and approximate topological, non-topological, singular, and periodic solitons solutions for the considered model. The 2D, 3D, and contour plots of the dynamical behaviors of some obtained results with fractional effects , in conformable sense, are illustrated. Furthermore, many other solution profiles can be obtained from our results with the open choices of parameters. The numerical sensitivity analysis of the regarding dynamical system is also discussed.