Fokas, A. S. (1980) A symmetry approach to exactly solvable evolution equations. Journal of Mathematical Physics, 21 (6). pp. 1318-1325. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:FOKjmp80
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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.|
|Subject Keywords:||SYMMETRY, NONLINEAR PROBLEMS, DIFFERENTIAL EQUATIONS, KORTEWEG−DE VRIES EQUATION, RECURSION RELATIONS|
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|Deposited On:||22 Dec 2008 18:36|
|Last Modified:||26 Dec 2012 10:39|
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