Linear Superposition of Quadratic Functions in a Fifth Order KdV-Type Equation

We show that a fifth order KdV-type equation admits several real as well as complex parity-time reversal or PT-invariant solutions with linear superposition of quadratic functions involving Jacobi elliptic functions of the form ${\mathrm{d}\mathrm{n}}^2(x,m)$, $\mathrm{c}\mathrm{n}(x,m)\mathrm{d}\mathrm{n}(x,m)$, $\mathrm{s}\mathrm{n}(x,m)\mathrm{c}\mathrm{n}(x,m)$ and $\mathrm{s}\mathrm{n}(x,m)\mathrm{d}\mathrm{n}(x,m)$. These results must be contrasted with only partial superposition of such functions in Korteweg-de Vries (KdV), ${\phi }^3$ and a few other nonlinear equations.