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One Symmetry Does Not Imply Integrability

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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 the symbolic method of Gel'fand-Dikii and p-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. Copyright 1998 Academic Press.

Document Type: Research Article

Affiliations: 1: Department of Mathematics, University of Utrecht, The Netherlands 2: Department of Mathematics and Computer Science, Vrije Universiteit, Amsterdam, The Netherlands

Publication date: June 1, 1998

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