On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices

Abstract

We consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number of degrees of freedom per unit cell. We analyse a mapping of the Fourier coefficients of the NLE solution. NLEs correspond to homoclinic points in the phase space of this map. Using dimensionality properties of separatrix manifolds of the mapping we show the persistence of NLE solutions under perturbations of the system, provided NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam chains we rigorously prove the existence of NLE solutions.

13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E, in press)

References in corpus (3)

• Conditions on the Existence of Localized Excitations in Nonlinear Discrete Systems
• Movability of Localized Excitations in Nonlinear Discrete Systems - a Separatrix Problem
• Localized Excitations in two-dimensional Hamiltonian Lattices

Cited by in corpus (23)

• Discrete Breathers
• Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
• Localized breathing solutions for Bose-Einstein condensates in periodic traps
• Discrete breathers in Fermi-Pasta-Ulam lattices
• Tangent Bifurcation of Band Edge Plane Waves, Dynamical Symmetry Breaking and Vibrational Localization
• Obtaining Breathers in Nonlinear Hamiltonian Lattices
• Energy Relaxation in Nonlinear One-Dimensional Lattices
• Bright and dark breathers in Fermi-Pasta-Ulam lattices
• Acoustic breathers in two-dimensional lattices
• Asymptotic Dynamics of Breathers in Fermi-Pasta-Ulam Chains
• Breathers and Thermal Relaxation in Fermi-Pasta-Ulam Arrays
• Dark breathers in Klein-Gordon lattices. Band analysis of their stability properties
• Discrete Breathers in Hexagonal Dusty Plasma Lattices
• Energy Relaxation in Fermi-Pasta-Ulam Arrays
• Tunneling of localized excitations: giant enhancement due to fluctuations
• Tunneling of quantum rotobreathers
• Existence of multi-site intrinsic localized modes in one-dimensional Debye crystals
• Nonlinear waves in Newton's cradle and the discrete p-Schroedinger equation
• Breather solutions of the discrete p-Schrödinger equation
• Discrete Breathers in Anisotropic Ferromagnetic Spin Chains
• Waves in Strongly Nonlinear Gardner-like Equations on a Lattice
• Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices
• Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction