Linear superposition for a class of nonlinear equations

We demonstrate a kind of linear superposition for a large number of nonlinear equations which admit elliptic function solutions, both continuum and discrete. In particular, we show that whenever a nonlinear equation admits solutions in terms of Jacobi elliptic functions cn(x,m) and dn(x,m), then it also admits solutions in terms of their sum as well as difference, i.e. dn(x,m)±mcn(x,m). Further, we also show that whenever a nonlinear equation admits a solution in terms of dn2(x,m), it also has solutions in terms of dn2(x,m)±mcn(x,m)dn(x,m) even though cn(x,m)dn(x,m) is not a solution of that nonlinear equation. Finally, we obtain similar superposed solutions in coupled theories.