Beukers, Frits, Sanders, Jan A., Wang, Jing Ping (1998) One symmetry does not imply integrability. Journal of Differential Equations, 146 (1). pp. 251-260. ISSN 0022-0396. (doi:10.1006/jdeq.1998.3426) (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) (KAR id:8140)
| 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. | |
| Official URL: http://dx.doi.org/10.1006/jdeq.1998.3426 |
Abstract
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 |
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| DOI/Identification number: | 10.1006/jdeq.1998.3426 |
| Subjects: | Q Science > QA Mathematics (inc Computing science) |
| Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
| Depositing User: | Jing Ping Wang |
| Date Deposited: | 25 Jun 2009 11:00 UTC |
| Last Modified: | 16 Nov 2021 09:46 UTC |
| Resource URI: | https://kar.kent.ac.uk/id/eprint/8140 (The current URI for this page, for reference purposes) |
University of Kent Author Information
Wang, Jing Ping.
| Creator's ORCID: |
 https://orcid.org/0000-0002-6874-5629
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