Existence and numerical approximation of periodic motions of an infinite lattice of particles (Q1905436)

The lattice is autonomous. Its particles interact with their nearest neighbours by a force belonging to a certain class characterized by the properties of the potential. Purely attractive forces are considered. Assumptions are given which admit a nonzero periodic non constant solution with finite energy. First, a finite system is considered, then an appropriate imbedding of this case in the infinite system is given and the limit process is taken. The application of a known algorithm is shown for finite lattices in the case of repulsive-attractive forces; investigating the infinite lattices a process of approximation in the proof is based on these results. Some numerical experiments for finite lattices are shown.