Nonlinear wave phenomena in Venus' ionosphere: Shock, anti-shock, periodic, and super-periodic structures near critical thresholds

We investigate nonlinear ion-acoustic waves in Venus's ionosphere, focusing on critical and supercritical regimes where traditional Burgers-type approximations break down. A generalized model is developed for a two-ion (O+–H+) plasma with (α,q)-distributed electrons at altitudes >200 km, yielding a novel quartic nonlinear evolution equation for higher-order wave dynamics. New analytical solutions obtained via the Jacobi-elliptic function expansion reveal: (i) enhanced shock/anti-shock structures, (ii) super-nonlinear periodic waves, and (iii) critical transitions at supercritical parameters. Phase-space and Lyapunov analyses demonstrate the structures' dependence on electron-density ratios, temperature asymmetries, and viscosity coefficients. Results show excellent agreement with Venus Express data, particularly for altitude-dependent O+ density variations, and reveal nonlinear behavior beyond standard theoretical descriptions.