Do All Integrable Equations Satisfy Integrability Criteria?. (20th May 2008)

• Record Type: Journal Article
• Authors: Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Carstea, A. S.
• Other Names: Melnik Roderick Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2008(2008)
• Publication Date: 2008-05-20
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2008/317520
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : At the price of sacrificing all suspense, we can already announce that the answer to the question of the title is "no." It is indeed our belief that one may find counterexamples to all integrability conjectures, unless one constrains the definition of integrability to the point that the integrability criterion becomes tautological. This review is devoted to a critical analysis of the situation.