Evolution of nonlinear waves influenced by geometry and nonconvexity in real fluids.

The evolution of weakly nonlinear waves in real fluids is studied using one-dimensional, unsteady Euler equations for planar and non-planar geometries, closed with the van der Waals equation of state. We examine regimes where the fundamental derivative changes sign twice, producing higher-order (quartic) nonlinearity. The evolutionary equation contains a nonconvex flux function, with geometric effects appearing as a time-dependent source term. Results show that the interaction between nonlinearity and geometry strongly affects wave propagation: in some cases, damping from the source term suppresses wave interactions and shock splitting, while at higher amplitudes, nonlinearity dominates and shock splitting reappears. The influence of real fluids is analyzed through van der Waals parameters.