Localized Excitations in two-dimensional Hamiltonian Lattices

Details Localized Excitations in two-dimensional Hamiltonian Lattices Localized Excitations in two-dimensional Hamiltonian Lattices

1994-07-27

arxiv.org/abs/cond-mat/9407108v1

Physics

Condensed Matter

LaTeX,20 pages, 11 figures available upon request, Phys.Rev.E accepted for publication

Scientific paper

10.1103/PhysRevE.50.2293

We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of nonlinearities. We connect the presence of these excitations with the existence of local integrability of the original N degree of freedom system. On the basis of this explanation we make several predictions about the existence and stability of these excitations. This work is an extension of previously published results on vibrational localization in one-dimensional nonlinear Hamiltonian lattices (Phys.Rev.E.49(1994)836). Thus we confirm earlier suggestions about the generic property of Hamiltonian lattices to exhibit localized excitations independent on the dimensionality of the lattice.

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