Existence and numerical approximation of periodic motions of an infinite lattice of particles
type: Item
instance of: scholarly article
title: Existence and numerical approximation of periodic motions of an infinite lattice of particles
zbMATH Open document ID: 0838.34046
DOI: 10.1007/BF00917876
author: Gianni Arioli
author: Filippo Gazzola
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1996-05-30T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 70F99
zbMATH DE Number: 831612
zbMATH Keywords: periodic non constant solution
zbMATH Keywords: infinite lattices
reviewed by: Á. P. Bosznay
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 831612