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Article: Product representations of periodic waves for the modified Korteweg-de Vries family of evolution equations

TitleProduct representations of periodic waves for the modified Korteweg-de Vries family of evolution equations
Authors
KeywordsElliptic functions
Evolution equations
Periodic waves
Issue Date2003
PublisherInstitute of Pure and Applied Physics. The Journal's web site is located at http://www.ipap.jp/jpsj/index.htm
Citation
Journal Of The Physical Society Of Japan, 2003, v. 72 n. 2, p. 273-279 How to Cite?
AbstractPeriodic waves for evolution equations of the modified Korteweg-de Vries (mKdV) family are expressed as products of elliptic functions. By employing the Hirota bilinear formulation, periodic waves of the single component mKdV with positive cubic nonlinearity are obtained as rational functions of Jacobi elliptic functions. Coupled mKdV systems with two and three components are treated. Dark or kink type solitary waves can exist for systems where the equation for each component is in the bright soliton regime. Finally, a coupled system of (2+1) (2 spatial and 1 temporal) dimensional evolution equations is studied. Periodic waves in terms of products of elliptic functions are also derived. The validity of these new solutions is verified independently by a computer algebra software whenever feasible. © 2003 The Physical Society of Japan.
Persistent Identifierhttp://hdl.handle.net/10722/76042
ISSN
2015 Impact Factor: 1.559
2015 SCImago Journal Rankings: 0.720
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChow, KWen_HK
dc.date.accessioned2010-09-06T07:17:03Z-
dc.date.available2010-09-06T07:17:03Z-
dc.date.issued2003en_HK
dc.identifier.citationJournal Of The Physical Society Of Japan, 2003, v. 72 n. 2, p. 273-279en_HK
dc.identifier.issn0031-9015en_HK
dc.identifier.urihttp://hdl.handle.net/10722/76042-
dc.description.abstractPeriodic waves for evolution equations of the modified Korteweg-de Vries (mKdV) family are expressed as products of elliptic functions. By employing the Hirota bilinear formulation, periodic waves of the single component mKdV with positive cubic nonlinearity are obtained as rational functions of Jacobi elliptic functions. Coupled mKdV systems with two and three components are treated. Dark or kink type solitary waves can exist for systems where the equation for each component is in the bright soliton regime. Finally, a coupled system of (2+1) (2 spatial and 1 temporal) dimensional evolution equations is studied. Periodic waves in terms of products of elliptic functions are also derived. The validity of these new solutions is verified independently by a computer algebra software whenever feasible. © 2003 The Physical Society of Japan.en_HK
dc.languageengen_HK
dc.publisherInstitute of Pure and Applied Physics. The Journal's web site is located at http://www.ipap.jp/jpsj/index.htmen_HK
dc.relation.ispartofJournal of the Physical Society of Japanen_HK
dc.subjectElliptic functionsen_HK
dc.subjectEvolution equationsen_HK
dc.subjectPeriodic wavesen_HK
dc.titleProduct representations of periodic waves for the modified Korteweg-de Vries family of evolution equationsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0031-9015&volume=72&issue=2&spage=273&epage=279&date=2003&atitle=Product+representations+of+periodic+waves+for+the+modified+Korteweg-de+Vries+family+of+evolution+equationsen_HK
dc.identifier.emailChow, KW:kwchow@hku.hken_HK
dc.identifier.authorityChow, KW=rp00112en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1143/JPSJ.72.273en_HK
dc.identifier.scopuseid_2-s2.0-0037239072en_HK
dc.identifier.hkuros79657en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0037239072&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume72en_HK
dc.identifier.issue2en_HK
dc.identifier.spage273en_HK
dc.identifier.epage279en_HK
dc.identifier.isiWOS:000181068200017-
dc.publisher.placeJapanen_HK
dc.identifier.scopusauthoridChow, KW=13605209900en_HK

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