Be careful with the Exp-function method

Details Be careful with the Exp-function method Be careful with the Exp-function method

2010-11-18

arxiv.org/abs/1011.4265v1

Commun. Nonlinear Sci. Numer. Simulat. 14 (2009) 1881-1890

Nonlinear Sciences

Exactly Solvable and Integrable Systems

21 pages

Scientific paper

10.1016/j.cnsns.2008.07.021

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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