Generation of localization in a discrete chain with periodic boundary conditions: Numerical and analytical results

Alexander F. Vakakis, Gary Salenger

Research output: Contribution to journalArticlepeer-review

Abstract

We study the generation of localization in a discrete chain composed of N subsystems and periodic boundary conditions. Strongly localized motions are studied; that is, time-periodic motions where nearly all of the energy is spatially confined to a single subsystem. For varying N, numerical results indicate that the strongly localized solutions are generated through a bifurcation from an in-phase spatially extended solution. However, in the limit as N → ∞, the bifurcation point tends to infinity, and a smooth transition from localization to nonlocalization occurs. We then present an analytic technique to complement the numerical results. It is based on the matching local asymptotic expansions of a solution branch using Fade approximants. This leads to global analytic representations of the considered solutions, valid over the entire range of the control parameter.

Original languageEnglish (US)
Pages (from-to)1730-1747
Number of pages18
JournalSIAM Journal on Applied Mathematics
Volume58
Issue number6
DOIs
StatePublished - 1998

Keywords

  • Fade approximations
  • Nonlinear localization

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Generation of localization in a discrete chain with periodic boundary conditions: Numerical and analytical results'. Together they form a unique fingerprint.

Cite this