Do All Integrable Evolution Equations Have the Painlevé Property?

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2007
• Main Authors: Tamizhmani, K.M., Grammaticos, B., Ramani, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147384
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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...