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

Abstract

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 ${\mathrm{dn}}^2(x,m)$, $\mathrm{cn}(x,m)\mathrm{dn}(x,m)$, $\mathrm{sn}(x,m)\mathrm{cn}(x,m)$ and $\mathrm{sn}(x,m)\mathrm{dn}(x,m)$. These results must be contrasted with only partial superposition of such functions in Korteweg-de Vries (KdV), ${\varphi }^3$ and a few other nonlinear equations.

9 pages, no figures