2007/06/19 by K. M. Tamizhmani, Basil Grammaticos, Alfred Ramani
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Nonlinear Waves and Solitons #math-ph #math.AP #math.MP #nlin.SI
paper · pdf · doi:10.3842/sigma.2007.073
published as SIGMA 3 (2007), 073, 6 pages · Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2007/06/19 · openalex publication_date 2007/06/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine whether the Painlev 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 Painlev property. The same question is addressed in a discrete setting where we show that there exist linearisable lattice equations which do not possess the singularity confinement property (again in analogy to the one-dimensional case).