Existence and stability of localized oscillations in 1-dimensional lattices with soft-spring and hard-spring potentials

Panagopoulos, P; Bountis, T; Skokos, C

dc.contributor.author	Panagopoulos, P	en
dc.contributor.author	Bountis, T	en
dc.contributor.author	Skokos, C	en
dc.date.accessioned	2014-03-01T01:20:26Z
dc.date.available	2014-03-01T01:20:26Z
dc.date.issued	2004	en
dc.identifier.issn	1048-9002	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15924
dc.subject	Coupling Constant	en
dc.subject	floquet theory	en
dc.subject	Indexing Method	en
dc.subject	Local Stability	en
dc.subject	Optical Waveguide	en
dc.subject	Parameter Space	en
dc.subject	Phase Space	en
dc.subject	Transport Properties	en
dc.subject	1 dimensional	en
dc.subject	Local Oscillator	en
dc.subject.classification	Acoustics	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Approximation theory	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Equations of motion	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Oscillations	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Resonance	en
dc.subject.other	Discrete breathers	en
dc.subject.other	Floquet theory	en
dc.subject.other	Localized oscillations	en
dc.subject.other	Smaller alignment index method	en
dc.subject.other	Lattice vibrations	en
dc.title	Existence and stability of localized oscillations in 1-dimensional lattices with soft-spring and hard-spring potentials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1115/1.1804997	en
heal.identifier.secondary	http://dx.doi.org/10.1115/1.1804997	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	In this paper we use the method of homoclinic orbits to study the existence and stability of discrete breathers, i.e., spatially localized and time-periodic oscillations of a class of one-dimensional (1D) nonlinear lattices. The localization can be at one or several sites and the 1D lattices we investigate here have linear interaction between nearest neighbors and a quartic on-site potential V(u)=1/2Ku 2±1/4u4, where the (+) sign corresponds to ""hard spring"" and (-) to ""soft spring"" interactions. These localized oscillations - when they are stable under small perturbations - are very important for physical systems because they seriously affect the energy transport properties of the lattice. Discrete breathers have recently been created and observed in many experiments, as, e.g., in the Josephson junction arrays, optical waveguides, and low-dimensional surfaces. After showing how to construct them, we use Floquet theory to analyze their linear (local) stability, along certain curves in parameter space (α, ω), where α is the coupling constant and ω the frequency of the breather. We then apply the Smaller Alignment Index method (SALI) to investigate more globally their stability properties in phase space. Comparing our results for the ± cases of V(u), we find that the regions of existence and stability of breathers of the ""hard spring"" lattice are considerably larger than those of the ""soft spring"" system. This is mainly due to the fact that the conditions for resonances between breathers and linear modes are much less restrictive in the former than the latter case. Furthermore, the bifurcation properties are quite different in the two cases: For example, the phenomenon of complex instability, observed only for the "" soft spring"" system, destabilizes breathers without giving rise to new ones, while the system with ""hard springs"" exhibits curves in parameter space along which the number of monodromy matrix eigenvalues on the unit circle is constant and hence breather solutions preserve their stability character. Copyright © 2004 by ASME.	en
heal.publisher	ASME-AMER SOC MECHANICAL ENG	en
heal.journalName	Journal of Vibration and Acoustics, Transactions of the ASME	en
dc.identifier.doi	10.1115/1.1804997	en
dc.identifier.isi	ISI:000226485400006	en
dc.identifier.volume	126	en
dc.identifier.issue	4	en
dc.identifier.spage	520	en
dc.identifier.epage	527	en