Solutions s_e of Eq. (19) as a function of ρ_t/ρ₀ (top panel), l_t/L (middle panel), and L/H (bottom panel). The expression l_t = 0.1 H in the top and bottom panels and ρ_t/ρ₀ = 100 in the middle panel. The solid lines correspond to stable solutions and dashed lines to unstable solutions. The thin vertical dashed lines correspond to the bifurcation values that have been calculated by solving Eqs. (19) and (20) simultaneously and coincide with the results in Eq. (32) (top panel), Eq. (33) (middle panel), and Eq. (34) (bottom panel).