Beukers, F. and Sanders, J.A. and Wang, J.P. (1998) One symmetry does not imply integrability. Journal of Differential Equations, 146 (1). pp. 251-260. ISSN 0022-0396.
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We show that Bakirov's counter-example (which had been checked by computer algebra methods up to order 53) to the conjecture that one nontrivial symmetry of an evolution equation implies infinitely many is indeed a counter-example. To prove this we use thesymbolic methodof Gel'fand–Dikii andp-adic analysis. We also formulate a conjecture to the effect that almost all equations in the family considered by Bakirov have at most finitely many symmetries. This conjecture depends on the solution of a diophantine problem, which we explicitly state.
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||Jing Ping Wang|
|Date Deposited:||25 Jun 2009 11:00|
|Last Modified:||14 Jan 2010 14:29|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/8140 (The current URI for this page, for reference purposes)|
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