Geometrical constraints imposed on higher dimensional harmonic lattices generally lead to nonlinear dynamical lattice models. Helical lattices obtained by such a procedure are shown to be described by sine- plus linear-lattice equations. The interplay between sinusoidal and quadratic potential terms in such models is shown to yield localized nonlinear modes identified as intrinsic resonant modes.
@article{arxiv.nlin/0412052,
title = {Nonlinear Lattices Generated from Harmonic Lattices with Geometric Constraints},
author = {S. Takeno and S. V. Dmitriev and P. G. Kevrekidis and A. R. Bishop},
journal= {arXiv preprint arXiv:nlin/0412052},
year = {2009}
}