Published June 1980
| Published
Journal Article
Open
A symmetry approach to exactly solvable evolution equations
- Creators
- Fokas, A. S.
Chicago
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Abstract
A method is developed for establishing the exact solvability of nonlinear evolution equations in one space dimension which are linear with constant coefficient in the highest-order derivative. The method, based on the symmetry structure of the equations, is applied to second-order equations and then to third-order equations which do not contain a second-order derivative. In those cases the most general exactly solvable nonlinear equations turn out to be the Burgers equation and a new third-order evolution equation which contains the Korteweg-de Vries (KdV) equation and the modified KdV equation as particular cases.
Additional Information
Copyright © 1980 American Institute of Physics. Received 27 December 1979; accepted for publication 7 March 1980. Research supported in part by NSF grant MES 78-0306 and by the Saul Kaplan Memorial Fund. The author thanks P.A. Lagerstrom for his comments on an early draft of this paper and for many interesting discussions. He also thanks A.C. Newell for suggesting to the author that he investigate whether (2.18) is related to the KdV or the modified KdV by means of a Bäcklund transformation.Attached Files
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Additional details
- Eprint ID
- 12743
- Resolver ID
- CaltechAUTHORS:FOKjmp80
- National Science Foundation
- MES 78-0306
- Saul Kaplan Memorial Fund, Caltech
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2008-12-22Created from EPrint's datestamp field
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2021-11-08Created from EPrint's last_modified field