Exact solutions for extended waves in 1d anharmonic lattices

A cyclic chain of n equal classic particles coupled by anharmonic forces ha s a set of extended vibrational modes, for which exact solutions are given. This requires for the power law of the forces certain conditions to be ful filled. Each mode is characterized by a wave number and the undulations of the particles depend on the total energy and on a new constant of motion th at formally expresses a kind of angular momentum. Exact solutions for n=7 w ith a twelfth power potential are discussed.