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Article: Two exact solutions of the Tzitzeica-Bullough-Dodd equation

TitleTwo exact solutions of the Tzitzeica-Bullough-Dodd equation
Authors
KeywordsDoubly Periodic Vortices
Solitons
Tzitzeica-Bullough-Dodd Equation
Issue Date2009
PublisherFreund Publishing House, Ltd. The Journal's web site is located at http://www.ijnsns.com/
Citation
International Journal Of Nonlinear Sciences And Numerical Simulation, 2009, v. 10 n. 7, p. 935-943 How to Cite?
AbstractThe Tzitzeica-Bullough-Dodd equation (TBD) occurs in many different fields, ranging from geometry of surfaces to gas dynamics. Two simple and direct methods, namely, the Hirota bilinear technique and the separation of variables approach, are employed to calculate expressions for a 4-soliton and doubly periodic arrays of vortices respectively. In terms of applications, the dependent variable in TBD can assume the role of a stream function in two dimensional hydrodynamics. The flow patterns associated with the latter solution will accordingly be periodic in two spatial directions. The stability of these toroidal flows is tested numerically by a semi-Lagrangian code developed by one of the authors (DG). The patterns appear to be stable and relax to an equilibrium configuration where the vorticity-stream function relationship is different from the conventional hyperbolic sine. © Freund Publishing House Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/157029
ISSN
2015 Impact Factor: 0.687
2015 SCImago Journal Rankings: 0.298
References

 

DC FieldValueLanguage
dc.contributor.authorChow, KWen_US
dc.contributor.authorYip, LPen_US
dc.contributor.authorGurarie, Den_US
dc.date.accessioned2012-08-08T08:45:01Z-
dc.date.available2012-08-08T08:45:01Z-
dc.date.issued2009en_US
dc.identifier.citationInternational Journal Of Nonlinear Sciences And Numerical Simulation, 2009, v. 10 n. 7, p. 935-943en_US
dc.identifier.issn1565-1339en_US
dc.identifier.urihttp://hdl.handle.net/10722/157029-
dc.description.abstractThe Tzitzeica-Bullough-Dodd equation (TBD) occurs in many different fields, ranging from geometry of surfaces to gas dynamics. Two simple and direct methods, namely, the Hirota bilinear technique and the separation of variables approach, are employed to calculate expressions for a 4-soliton and doubly periodic arrays of vortices respectively. In terms of applications, the dependent variable in TBD can assume the role of a stream function in two dimensional hydrodynamics. The flow patterns associated with the latter solution will accordingly be periodic in two spatial directions. The stability of these toroidal flows is tested numerically by a semi-Lagrangian code developed by one of the authors (DG). The patterns appear to be stable and relax to an equilibrium configuration where the vorticity-stream function relationship is different from the conventional hyperbolic sine. © Freund Publishing House Ltd.en_US
dc.languageengen_US
dc.publisherFreund Publishing House, Ltd. The Journal's web site is located at http://www.ijnsns.com/en_US
dc.relation.ispartofInternational Journal of Nonlinear Sciences and Numerical Simulationen_US
dc.subjectDoubly Periodic Vorticesen_US
dc.subjectSolitonsen_US
dc.subjectTzitzeica-Bullough-Dodd Equationen_US
dc.titleTwo exact solutions of the Tzitzeica-Bullough-Dodd equationen_US
dc.typeArticleen_US
dc.identifier.emailChow, KW:kwchow@hku.hken_US
dc.identifier.authorityChow, KW=rp00112en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1515/IJNSNS.2009.10.7.935-
dc.identifier.scopuseid_2-s2.0-70349583064en_US
dc.identifier.hkuros170608-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-70349583064&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume10en_US
dc.identifier.issue7en_US
dc.identifier.spage935en_US
dc.identifier.epage943en_US
dc.publisher.placeIsraelen_US
dc.identifier.scopusauthoridChow, KW=13605209900en_US
dc.identifier.scopusauthoridYip, LP=18039044200en_US
dc.identifier.scopusauthoridGurarie, D=6602858506en_US

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