Do All Integrable Evolution Equations Have the Painlevé Property?

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2007
• Hauptverfasser: Tamizhmani, K.M., Grammaticos, B., Ramani, A.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2007
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147384
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Do All Integrable Evolution Equations Have the Painlevé Property? / K.M. Tamizhmani, B. Grammaticos, A. Ramani // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 17 назв. — англ.

We examine whether the Painlevé property is necessary for the integrability of partial differential equations (PDEs). We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of PDEs, integrable through linearisation, which do not possess the...