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Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation

Akhmediev, Nail; Ankiewicz, Adrian

Description

We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a

dc.contributor.authorAkhmediev, Nail
dc.contributor.authorAnkiewicz, Adrian
dc.date.accessioned2015-12-10T23:36:58Z
dc.identifier.issn1539-3755
dc.identifier.urihttp://hdl.handle.net/1885/70364
dc.description.abstractWe study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a
dc.publisherAmerican Physical Society
dc.rightsCopyright Information: © 2011 American Physical Society. http://www.sherpa.ac.uk/romeo/issn/1539-3755/..."Publisher's version/PDF may be used. On author's personal website, employer's website or institutional repository" from SHERPA/RoMEO site (as at 16/0
dc.rightsAuthor/s retain copyright
dc.sourcePhysical Review E-Statistical, Nonlinear and Soft Matter Physics
dc.subjectKeywords: Background field; Exact solution; Fermi-Pasta-Ulam paradoxes; Field state; First-order; Initial perturbation; Modulation instabilities; Nonlinear evolutions; Nonlinear phase shift; Periodic solution; Rational solution; Rogue waves; Phase shift; Nonlinear
dc.titleModulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume83
dc.date.issued2011
local.identifier.absfor010502 - Integrable Systems (Classical and Quantum)
local.identifier.absfor010204 - Dynamical Systems in Applications
local.identifier.absfor029902 - Complex Physical Systems
local.identifier.ariespublicationf2965xPUB2300
local.type.statusPublished Version
local.contributor.affiliationAkhmediev, Nail, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationAnkiewicz, Adrian, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue046603
local.bibliographicCitation.startpage1
local.bibliographicCitation.lastpage10
local.identifier.doi10.1103/PhysRevE.83.046603
local.identifier.absseo970102 - Expanding Knowledge in the Physical Sciences
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2016-02-24T08:24:41Z
local.identifier.scopusID2-s2.0-79961059929
local.identifier.thomsonID000290116400004
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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