Linear superposition for a class of nonlinear equations

Abstract

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 and , then it also admits solutions in terms of their sum as well as difference, i.e. . Further, we also show that whenever a nonlinear equation admits a solution in terms of , it also has solutions in terms of even though is not a solution of that nonlinear equation. Finally, we obtain similar superposed solutions in coupled theories.