A symmetry approach to exactly solvable evolution equations

A. S. Fokas

Type: Article

Publication Date: 1980-06-01

Citations: 243

DOI: https://doi.org/10.1063/1.524581

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.

Locations

Journal of Mathematical Physics - View
CaltechAUTHORS (California Institute of Technology) - View - PDF

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