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

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 $\text{cn}(x,m)$ and $\text{dn}(x,m)$, then the same nonlinear equation will necessarily also have solutions in terms of $\text{dn}(x,m)\pm \sqrt{m}\text{cn}(x,m)$. We point out the flaw in their argument and show why our assertion is indeed valid.