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The higher dimensional Bateman equation and Pailevé analysis of nonintegrable wave equations
Luleå tekniska universitet.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
1997 (English)In: Proceedings of the second international conference: Memorial Prof. W. Fushchych conference, July 7 - 13, 1997, Kyiv, Ukraine / [ed] Mykola Shkil, Kyev: Institute of Mathematics of the National Academy of Sciences of Ukraine , 1997, Vol. 1, 185-192 p.Conference paper (Refereed)
Abstract [en]

The paper starts with recalling the basics of the Painlevé analysis and its applications to the construction of particular solutions to nonintegrable equations. Next, the authors recall known facts on the Bateman equation in the space of $n$ independent variables and establish some properties of its solutions. It is further shown that the singular manifold equations, arising in the process of singularity analysis of the $n$-dimensional ($n\geq 2$ for double sine-Gordon and $n\geq 3$ for other equations) versions of Liouville, Tzitzéika-Mikhailov, sine-Gordon and double sine-Gordon equations, are equivalent to the Bateman equation. It is also proved that the general solution of the 2-dimensional Bateman equation satisfies the singular manifold equations for the equations $\partial^{2}u/\partial x\partial t+u^{k}=0$, $k\geq 2$.

Place, publisher, year, edition, pages
Kyev: Institute of Mathematics of the National Academy of Sciences of Ukraine , 1997. Vol. 1, 185-192 p.
Research subject
URN: urn:nbn:se:ltu:diva-38611Local ID: d0e4efd0-9bfc-11db-8975-000ea68e967bISBN: 966-02-0343-8OAI: diva2:1012112
International Conference Symmetry in Nonlinear Mathematical Physics : 07/07/1997 - 13/07/1997
Godkänd; 1997; 20061221 (kani)Available from: 2016-10-03 Created: 2016-10-03Bibliographically approved

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