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Infinitely extended complex KdV equation and its solutions: solitons and rogue waves

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Ankiewicz, Adrian; Bokaeeyan, Mahyar; Akhmediev, Nail

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We present an infinitely-extended KdV equation that contains an infinite number of arbitrary real coefficients controlling higher-order terms in the extended evolution equation. The higher-order terms are chosen in a way that maintains the integrability of the whole equation. Another significant step in this work is that this extended equation admits complex-valued solutions. This generalization allows us to consider both solitons and rogue waves in the form of rational solutions of this...[Show more]

dc.contributor.authorAnkiewicz, Adrian
dc.contributor.authorBokaeeyan, Mahyar
dc.contributor.authorAkhmediev, Nail
dc.date.accessioned2020-07-22T01:50:29Z
dc.identifier.citationA Ankiewicz et al 2020 Phys. Scr. 95 035201
dc.identifier.issn0031-8949
dc.identifier.urihttp://hdl.handle.net/1885/206494
dc.description.abstractWe present an infinitely-extended KdV equation that contains an infinite number of arbitrary real coefficients controlling higher-order terms in the extended evolution equation. The higher-order terms are chosen in a way that maintains the integrability of the whole equation. Another significant step in this work is that this extended equation admits complex-valued solutions. This generalization allows us to consider both solitons and rogue waves in the form of rational solutions of this equation. Special choices of the arbitrary coefficients lead to particular cases - the basic KdV and its higher-order versions. Using the extended KdV, instead of the basic one, may improve the accuracy of the description of rogue waves in shallow water.
dc.description.sponsorshipThe authors acknowledge the support of the Australian Research Council (ARC).
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherRoyal Swedish Academy of Sciences
dc.rights© 2020 IOP Publishing Ltd
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/3.0/
dc.sourcePhysica Scripta
dc.subjectKdV equation
dc.subjectshallow water
dc.subjecthigher order equations
dc.subjectsolitons
dc.subjectrogue waves
dc.titleInfinitely extended complex KdV equation and its solutions: solitons and rogue waves
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume95
dcterms.dateAccepted2019-10-30
dc.date.issued2020-01-29
local.identifier.absfor020303 - Fluid Physics
local.identifier.absfor010502 - Integrable Systems (Classical and Quantum)
local.identifier.absfor020504 - Photonics, Optoelectronics and Optical Communications
local.identifier.ariespublicationu9912193xPUB504
local.publisher.urlhttps://iopscience.iop.org/
local.type.statusPublished Version
local.contributor.affiliationAnkiewicz, Adrian, College of Science, ANU
local.contributor.affiliationBokaeeyan, Mahyar, College of Science, ANU
local.contributor.affiliationAkhmediev, Nail, College of Science, ANU
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage1
local.bibliographicCitation.lastpage7
local.identifier.doi10.1088/1402-4896/ab5290
local.identifier.absseo890199 - Communication Networks and Services not elsewhere classified
local.identifier.absseo970102 - Expanding Knowledge in the Physical Sciences
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2021-12-02T05:06:58Z
local.identifier.scopusID2-s2.0-85079905881
local.identifier.thomsonID000510206600001
dcterms.accessRightsOpen Access
dc.provenancehttp://v2.sherpa.ac.uk/id/publication/11345..."Author accepted manuscript can be made open access on non-commercial institutional repository after 12 month embargo with CC BY-NC-ND 3.0 license" from SHERPA/RoMEO site (as at 3/8/20)
dc.rights.licenseCC BY-NC-ND 3.0
CollectionsANU Research Publications

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