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Volume 8, Issue 4, November 2001, Pages 561 - 574
On Testing Integrability
Authors
Peter H. van der Kamp, Jan A. Sanders
Corresponding Author
Peter H. van der Kamp
Received 19 June 2001, Accepted 27 July 2001, Available Online 1 November 2001.
- DOI
- 10.2991/jnmp.2001.8.4.8How to use a DOI?
- Abstract
We demonstrate, using the symbolic method together with p-adic and resultant methods, the existence of systems with exactly one or two generalized symmetries. Since the existence of one or two symmetries is often taken as a sure sign (or as the definition) of integrability, that is, the existence of symmetries on infinitely many orders, this shows that such practice is devoid of any mathematical foundation. Etensive computations show that systems with one symmetry are rather common, and with two symmetries are fairly rare, at least within the class we have been considering in this paper.
- Copyright
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Cite this article
TY - JOUR AU - Peter H. van der Kamp AU - Jan A. Sanders PY - 2001 DA - 2001/11/01 TI - On Testing Integrability JO - Journal of Nonlinear Mathematical Physics SP - 561 EP - 574 VL - 8 IS - 4 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2001.8.4.8 DO - 10.2991/jnmp.2001.8.4.8 ID - Kamp2001 ER -