Localized Excitations in two-dimensional Hamiltonian Lattices

TL;DR

This paper investigates the origin, features, and stability of localized excitations in two-dimensional nonlinear Hamiltonian lattices, extending previous one-dimensional results and linking localization to local integrability.

Contribution

It connects localized excitations with local integrability in 2D Hamiltonian lattices and predicts their existence and stability, extending prior 1D findings.

Findings

Localized excitations exist due to nonlinearities.

Localization is linked to local integrability.

Localized excitations are a generic property of Hamiltonian lattices.

Abstract

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.