Be careful with the Exp-function method
By N. Kudryashov, Nadejda B. Loguinova. 2009
151 citations recorded by the source corpus.
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 simplest equation method is introduced. This approach is used to look for exact solutions of the generalized Korteweg–de Vries equation.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/afd0848cc46921167e243154932cb80de2268fc0
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In Atomic and Molecular Physics, and Optics
In Statistical and Nonlinear Physics
Citations in the corpus
- Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs (2011, methodology): “Finally, we would like to note two of the papers of Kudryashov [64,65] who advises us to be careful when use the methods for obtaining of exact solutions of the nonlinear differential equations.”
- Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity (2010, methodology): “Finally, we would like to note two of the papers of Kudryashov [39,40] who advises us to be careful when using the methods for obtaining of exact solutions of the nonlinear differential equations.”
- Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics (2010, methodology): “Finally, we would like to note two of the papers of Kudryashov [59,60] who advises us to be careful when use the methods for obtaining of exact solutions of the nonlinear differential equations.”