Schematic illustration of the flow of characteristics C ⁺ in FFE and MHD, shown in the t–ξ plane. Each C ⁺ has its initial position ξ _i and carries a value of ﹩K({\xi }_{{\rm{i}}})={rE}/\mu ﹩ determined by the initial wave profile. In the FFE limit, the characteristics are vertical straight lines; they propagate with speed β ₊ = 1, which corresponds to d ξ ₊/dt = 0. The MHD correction to FFE implies d ξ ₊/dt = 1 − β ₊ ≠ 0, so the C ⁺ characteristics are no longer static in ξ; they become significantly bent in the region where E ² approaches B ², leading to the formation of a shock (red curve).