Linear Superposition for a Large Number of Nonlinear Equations

We demonstrate a kind of linear superposition for a large number of nonlinear equations, both continuum and discrete. In particular, we show that whenever a nonlinear equation admits solutions in terms of Jacobi elliptic functions $\text{cn}(x,m)$ and $\text{dn}(x,m)$, then it also admits solutions in terms of their sum as well as difference, i.e. $\text{dn}(x,m)\pm \sqrt{m}\text{cn}(x,m)$. Further, we also show that whenever a nonlinear equation admits a solution in terms of ${\text{dn}}^2(x,m)$, it also has solutions in terms of $\dn^2(x,m) \pm \sqrt{m}, \cn(x,m), \dn(x,m)$eventhough$\cn(x,m), \dn(x,m)$ is not a solution of that nonlinear equation. Finally, we obtain similar superposed solutions in coupled theories.