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Exactly Solvable and Integrable Systems

arXiv:solv-int/9411002 (solv-int)
[Submitted on 14 Nov 1994]

Title:On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices

Authors:S. Flach
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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.
Comments: 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E, in press)
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:solv-int/9411002
  (or arXiv:solv-int/9411002v1 for this version)
  https://doi.org/10.48550/arXiv.solv-int/9411002
Related DOI: https://doi.org/10.1103/PhysRevE.51.1503

Submission history

From: Sergej Flach [view email]
[v1] Mon, 14 Nov 1994 23:25:24 UTC (9 KB)
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