  We study tangent bifurcation of band edge plane waves in nonlinear
Hamiltonian lattices. The lattice is translationally invariant. We argue for
the breaking of permutational symmetry by the new bifurcated periodic orbits.
The case of two coupled oscillators is considered as an example for the
perturbation analysis, where the symmetry breaking can be traced using Poincare
maps. Next we consider a lattice and derive the dependence of the bifurcation
energy on the parameters of the Hamiltonian function in the limit of large
system sizes. A necessary condition for the occurence of the bifurcation is the
repelling of the band edge plane wave's frequency from the linear spectrum with
increasing energy. We conclude that the bifurcated orbits will consequently
exponentially localize in the configurational space.
