Be careful with the Exp-function method
Exactly Solvable and Integrable Systems
2010-11-19 v1
Abstract
An application of the Exp-function method to search for exact solutions of nonlinear differential equations is analyzed. Typical mistakes of application of the Exp-function method are demonstrated. We show it is often required to simplify the exact solutions obtained. Possibilities of the Exp-function method and other approaches in mathematical physics are discussed. The application of the singular manifold method for finding exact solutions of the Fitzhugh - Nagumo equation is illustrated. The modified simple equation method is introduced. This approach is used to look for exact solutions of the generalized Korteweg - de Vries equation.
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Cite
@article{arxiv.1011.4265,
title = {Be careful with the Exp-function method},
author = {Nikolay A. Kudryashov and Nadejda B. Loguinova},
journal= {arXiv preprint arXiv:1011.4265},
year = {2010}
}
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21 pages