\[\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}\operatorname{cn}\left(z,k\right)=-(%
{k^{\prime}}^{2}-k^{2})\operatorname{cn}\left(z,k\right)-2k^{2}{\operatorname{%
cn}}^{3}\left(z,k\right),\]