On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices

Details On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices

1994-11-14

arxiv.org/abs/solv-int/9411002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1103/PhysRevE.51.1503

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.

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