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On the Integrability of Non-Polynomial Scalar Evolution Equations

Sanders, Jan A., Wang, Jing Ping (2000) On the Integrability of Non-Polynomial Scalar Evolution Equations. Journal of Differential Equations, 166 (1). pp. 132-150. ISSN 0022-0396. (doi:10.1006/jdeq.2000.3782) (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:8833)

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.2000.3782

Abstract

We show the existence of infinitely many symmetries for ?-homogeneous equations when ?=0. If the equation has one generalized symmetry, we prove that it has infinitely many and these can be produced by recursion operators. Identifying equations under homogeneous transformations, we find that the only integrable equations in this class are the Potential Burgers, Potential Modified Korteweg–de Vries, and Potential Kupershmidt Equations. We can draw some conclusions from these results for the case ?=?1 which, although theoretically incomplete, seem to cover the known integrable systems for this case.

Item Type: Article
DOI/Identification number: 10.1006/jdeq.2000.3782
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: 26 May 2009 20:00 UTC
Last Modified: 16 Nov 2021 09:46 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/8833 (The current URI for this page, for reference purposes)

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