  Landen formulas, which connect Jacobi elliptic functions with different
modulus parameters, were first obtained over two hundred years ago by making a
suitable quadratic transformation of variables in elliptic integrals. We obtain
and discuss significant generalizations of the celebrated Landen formulas. Our
approach is based on some recently obtained periodic solutions of physically
interesting nonlinear differential equations and numerous remarkable new cyclic
identities involving Jacobi elliptic functions.
