Reply to the Comment by Zhang and Li [J. Math. Phys. 56, 084101, 2015] on the Paper [J. Math. Phys. {\bf 56}, 032104, 2015]}

Abstract

In a recent paper Zhang and Li have doubted our claim that whenever a nonlinear equation has solutions in terms of the Jacobi elliptic functions $\cn(x,m)$ and $\dn(x,m)$, then the same nonlinear equation will necessarily also have solutions in terms of $\dn(x,m) \pm \sqrt{m} \cn(x,m)$. We point out the flaw in their argument and show why our assertion is indeed valid.