Do All Integrable Evolution Equations Have the Painlevé Property?
Copyright policy )Do All Integrable Evolution Equations Have the Painlevé Property?
We examine whether the Painleve 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 Painleve 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).
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
- French National Centre for Scientific Research France
- École Polytechnique France
- University of Paris France
- Pondicherry University India
- Center of Theoretical Physics France
singularity confinement, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Mathematical Physics (math-ph), integrability, Singularity in context of PDEs, linearisability, Other completely integrable PDE, Mathematics - Analysis of PDEs, QA1-939, FOS: Mathematics, Painlevé property, Exactly Solvable and Integrable Systems (nlin.SI), linearisable lattice equations, Mathematics, Mathematical Physics, Analysis of PDEs (math.AP)
singularity confinement, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, Mathematical Physics (math-ph), integrability, Singularity in context of PDEs, linearisability, Other completely integrable PDE, Mathematics - Analysis of PDEs, QA1-939, FOS: Mathematics, Painlevé property, Exactly Solvable and Integrable Systems (nlin.SI), linearisable lattice equations, Mathematics, Mathematical Physics, Analysis of PDEs (math.AP)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!