Superposition of elliptic functions as solutions for a large number of nonlinear equations

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrodinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrodinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrodinger equation, lambda phi(4), the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn(2)(x, m), it also admits solutions in terms of dn(2)(x, m) +/- root mcn(x, m)dn(x, m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations. (C) 2014 AIP Publishing LLC.