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Article: A class of doubly periodic waves for nonlinear evolution equations

TitleA class of doubly periodic waves for nonlinear evolution equations
Authors
Issue Date2002
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/wamot
Citation
Wave Motion, 2002, v. 35 n. 1, p. 71-90 How to Cite?
AbstractA class of doubly periodic waves for several nonlinear evolution equations is studied by the Hirota bilinear method. Analytically these waves can be expressed as rational functions of elliptic functions with different moduli, and may correspond to standing as well as propagating waves. The two moduli are related by a condition determined as part of the solution process, and the condition translates into constraints on the wavenumbers allowed. Such solutions for the nonlinear Schrödinger equation agree with results derived earlier in the literature by a different method. The present method of combining the Hirota method, elliptic and theta functions is applicable to a wider class of equations, e.g., the Davey-Stewartson, the sinh-Poisson and the higher dimensional sine-Gordon equations. A long wave limit is studied for these special doubly periodic solutions of the Davey-Stewartson and Kadomtsev-Petviashvili equations, and the results are the generation of new solutions and the emergence of the component solitons as the fundamental building blocks, respectively. The validity of these doubly periodic solutions is verified by MATHEMATICA. © 2002 Elsevier Science B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75621
ISSN
2015 Impact Factor: 1.449
2015 SCImago Journal Rankings: 0.668
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChow, KWen_HK
dc.date.accessioned2010-09-06T07:12:58Z-
dc.date.available2010-09-06T07:12:58Z-
dc.date.issued2002en_HK
dc.identifier.citationWave Motion, 2002, v. 35 n. 1, p. 71-90en_HK
dc.identifier.issn0165-2125en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75621-
dc.description.abstractA class of doubly periodic waves for several nonlinear evolution equations is studied by the Hirota bilinear method. Analytically these waves can be expressed as rational functions of elliptic functions with different moduli, and may correspond to standing as well as propagating waves. The two moduli are related by a condition determined as part of the solution process, and the condition translates into constraints on the wavenumbers allowed. Such solutions for the nonlinear Schrödinger equation agree with results derived earlier in the literature by a different method. The present method of combining the Hirota method, elliptic and theta functions is applicable to a wider class of equations, e.g., the Davey-Stewartson, the sinh-Poisson and the higher dimensional sine-Gordon equations. A long wave limit is studied for these special doubly periodic solutions of the Davey-Stewartson and Kadomtsev-Petviashvili equations, and the results are the generation of new solutions and the emergence of the component solitons as the fundamental building blocks, respectively. The validity of these doubly periodic solutions is verified by MATHEMATICA. © 2002 Elsevier Science B.V. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/wamoten_HK
dc.relation.ispartofWave Motionen_HK
dc.rightsWave Motion. Copyright © Elsevier BV.en_HK
dc.titleA class of doubly periodic waves for nonlinear evolution equationsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0165-2125&volume=35&spage=71&epage=90&date=2002&atitle=A+class+of+doubly+periodic+waves+for+nonlinear+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.doi10.1016/S0165-2125(01)00078-6en_HK
dc.identifier.scopuseid_2-s2.0-0036132365en_HK
dc.identifier.hkuros69286en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0036132365&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume35en_HK
dc.identifier.issue1en_HK
dc.identifier.spage71en_HK
dc.identifier.epage90en_HK
dc.identifier.isiWOS:000172370400005-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridChow, KW=13605209900en_HK

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