One symmetry does not imply integrability

Beukers, Frits and Sanders, Jan A. and Wang, Jing Ping (1998) One symmetry does not imply integrability. Journal of Differential Equations, 146 (1). pp. 251-260. ISSN 0022-0396. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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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.

Item Type: Article
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: 11 Jun 2014 09:08
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