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Be careful with the Exp-function method. (English) Zbl 1221.35344
Summary: An application of the Exp-function method to search for exact solutions of nonlinear differential equations is analyzed. Typical mistakes in application of the Exp-function method are demonstrated. We show that simplification of the exact solutions obtained is often required. 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 simplest equation method is introduced. This approach is used to look for exact solutions of the generalized Korteweg-de Vries equation.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form