Discrete breathers in two-dimensional nonlinear lattices

Abstract

Properties of discrete breathers in two- and three-dimensional nonlinear lattice models are discussed with special emphasis on possible structures of localization in two-dimensional case. In contrast to the extensive studies addressing the various features of discrete breathers in one-dimensional lattices, less studies have been done in regard to the higher dimensional breathers. To begin with a brief survey of existing results for discrete breathers in higher dimensional lattices, we attempt to look into the possible structures of higher dimensional breathers. Based on the survey, we address the following topics concerning the discrete breathers in two-dimensional lattices: types of localized structures; chaotic breathers; quasi-continuum approximation; discrete breathers versus solitons in continuum.