Bright and dark breathers in Fermi-Pasta-Ulam lattices

Abstract

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, {\em C. R. Acad. Sci. Paris}, 332, Ser. 1, pp. 581 (2001)] using numerical computations. Approximate analytical expressions for small amplitude bright and dark breathers are found to fit very well exact numerical solutions even far from the top of the phonon band. On the other hand, we study numerically large amplitude breathers non predicted in the above cited reference. In particular, for a class of asymmetric FPU potentials we find an energy threshold for the existence of exact discrete breathers, which is a relatively unexplored phenomenon in one-dimensional lattices. Bright and dark breathers superposed on a uniformly stressed static configuration are also investigated.

arXiv comment11 pages, 16 figures

References in corpus (8)

• Discrete Breathers
• Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
• Excitation Thresholds for Nonlinear Localized Modes on Lattices
• On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices
• Standing wave instabilities in a chain of nonlinear coupled oscillators
• Tangent Bifurcation of Band Edge Plane Waves, Dynamical Symmetry Breaking and Vibrational Localization
• Energy thresholds for discrete breathers
• Dark breathers in Klein-Gordon lattices. Band analysis of their stability properties

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• Dark Breathers in Granular Crystals
• Energy criterion for the spectral stability of discrete breathers
• Experimental and numerical observation of dark and bright discrete solitons in the band-gap of a diatomic-like electrical lattice
• Discrete moving breather collisions in a Klein-Gordon chain of oscillators
• The origin of defects induced in ultra-pure germanium by Electron Beam Deposition
• Discrete breathers in a mechanical metamaterial
• Thermal lifetime of breathers
• Classical and quantum nonlinear localized excitations in discrete systems
• Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction