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) +/- root m cn(x, m). Further, we also show that whenever a nonlinear equation admits a solution in terms of dn(2)(x, m), it also has solutions in terms of dn(2)(x, m) +/- root m cn(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. (C) 2013 Elsevier B.V. All rights reserved.