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n-dimensional Bateman equation and Painlevé analysis of wave equations
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-0370-7274
Luleå University of Technology.
2000 (English)In: International Journal of Differential Equations and Applications, ISSN 1311-2872, Vol. 1, no 2, p. 205-222Article in journal (Refereed) Published
Abstract [en]

In the Painlevé analysis of nonintegrable partial differential equations one obtains differential constraints describing the movable singularity manifold. We show that, for a class of $n$-dimensional wave equations, these constraints have a general structure which is related to the $n$-dimensional Bateman equation. In particular, we derive the expressions of the singularity manifold constraint for the $n$-dimensional sine-Gordon, Liouville, Mikhailov, and double sine-Gordon equations, as well as two 2-dimensional polynomial field theory equations, and prove that their singularity manifold conditions are satisfied by the $n$-dimensional Bateman equation. Finally, we give some examples and applications of this property.

Place, publisher, year, edition, pages
2000. Vol. 1, no 2, p. 205-222
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-13185Local ID: c5f48110-b071-11db-840a-000ea68e967bOAI: oai:DiVA.org:ltu-13185DiVA, id: diva2:986137
Note
Godkänd; 2000; 20061222 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-03-08Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf