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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.
Luleå University of Technology.
2000 (English)In: International Journal of Differential Equations and Applications, ISSN 1311-2872, Vol. 1, no 2, 205-222 p.Article 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, 205-222 p.
Research subject
URN: urn:nbn:se:ltu:diva-13185Local ID: c5f48110-b071-11db-840a-000ea68e967bOAI: diva2:986137
Godkänd; 2000; 20061222 (kani)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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Euler, Norbert
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