Publication:
Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach

Simple item page
dc.contributor.authorParker, Ross
dc.contributor.authorCuevas-Maraver, Jesús
dc.contributor.authorKevrekidis, Panayotis G.
dc.contributor.authorAceves, Alejandro
dc.contributor.departmentSouthern Methodist University
dc.contributor.departmentUniversity of Seville
dc.contributor.departmentUniversity of Massachusetts Amherst
dc.contributor.departmentSouthern Methodist University
dc.date2023-09-24T09:33:02.000
dc.date.accessioned2024-04-26T18:39:55Z
dc.date.available2022-12-19T00:00:00Z
dc.date.issued2022-01-01
dc.description.abstractWe consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a finite-dimensional Hilbert space consisting of the first M Fourier modes, for arbitrary M. On this approximate system, we then take a spatial dynamics approach and use Lin's method to construct multi-breathers from a sequence of well-separated copies of the primary, single-site breather. We then locate the eigenmodes in the Floquet spectrum associated with the interaction between the individual breathers of such multi-breather states by reducing the spectral problem to a matrix equation. Expressions for these eigenmodes for the approximate, finite-dimensional system are obtained in terms of the primary breather and its kernel eigenfunctions, and these are found to be in very good agreement with the numerical Floquet spectrum results. This is supplemented with results from numerical timestepping experiments, which are interpreted using the spectral computations.
dc.identifier.doihttps://doi.org/10.48550/arXiv.2204.11349
dc.identifier.urihttps://hdl.handle.net/20.500.14394/34394
dc.relation.ispartofarXiv Preprint
dc.relation.urlhttps://scholarworks.umass.edu/cgi/viewcontent.cgi?article=2340&context=math_faculty_pubs&unstamped=1
dc.rightsUMass Amherst Open Access Policy
dc.source.statuspublished
dc.titleRevisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach
dc.typearticle
dc.typearticle
digcom.contributor.authorParker, Ross
digcom.contributor.authorCuevas-Maraver, Jesús
digcom.contributor.authorisAuthorOfPublication|email:kevrekid@math.umass.edu|institution:University of Massachusetts Amherst|Kevrekidis, Panayotis G.
digcom.contributor.authorAceves, Alejandro
digcom.date.embargo2022-12-19T00:00:00-08:00
digcom.identifiermath_faculty_pubs/1334
digcom.identifier.contextkey32801383
digcom.identifier.submissionpathmath_faculty_pubs/1334
dspace.entity.typePublication
relation.isAuthorOfPublication97bd8a53-35a3-40f5-b764-a518420ea82b
relation.isAuthorOfPublication.latestForDiscovery97bd8a53-35a3-40f5-b764-a518420ea82b
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
2204.11349.pdf
Size:
3.33 MB
Format:
Adobe Portable Document Format
Thumbnail Image
Name: 2204.11349.pdf
Size: 3.33 MB
Kind: Adobe PDF
Collections
Mathematics and Statistics Department Faculty Publication Series