Publication Cover
Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 14
84
Views
1
CrossRef citations to date
0
Altmetric
Articles

Existence of breathing patterns in globally coupled finite-size nonlinear lattices

ORCID Icon
Pages 2511-2524 | Received 21 Jul 2017, Accepted 11 Apr 2018, Published online: 25 Apr 2018
 

ABSTRACT

We prove the existence of time-periodic solutions representing breathing patterns in general nonlinear Hamiltonian finite-size lattices with global coupling. As a first step the existence of localised solutions of a two site segment, where one oscillator performs larger-amplitude motion compared to the other one, is established. To this end the existence problem is converted into a fixed point problem for an operator on some appropriate function space which is solved by means of Schauder’s Fixed Point Theorem. For isoenergetic states the degree of localisation can be tuned in a wide range by changing the initial data and the coupling strength. Subsequently, it is proven that a related localised state can be excited in the extended nonlinear lattice forming a breathing pattern with a single site of large amplitude against a background of uniform small-amplitude states. Furthermore, it is demonstrated that also spatial patterns are possible that are built up from any combination of the small-amplitude state and the large-amplitude state.

AMS SUBJECT CLASSIFICATIONS:

Notes

No potential conflict of interest was reported by the author.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 1,361.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.