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