Spatial profiles across the transition region of the equilibrium mass density, ρ₀(y)/ρ_0c, Alfvén speed, v_A(y), transverse displacement, ξ_⊥/ξ₀, derivative of the transverse displacement, ∂/∂y(ξ_⊥/ξ₀), the acoustic coupling term, , and the longitudinal displacement, ξ_∥/ξ₀. The vertical dashed and dotted lines indicate the positions y₀ and y₀ ± Δy, respectively. The blue and red curves are the wave solutions for a density contrast ζ = 10 and 1000, respectively.