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Zbl 1069.35018
Kudryashov, Nikolai A.
Simplest equation method to look for exact solutions of nonlinear differential equations. (English)
[J] Chaos Solitons Fractals 24, No. 5, 1217-1231 (2005). ISSN 0960-0779

Summary: A new method is presented for the search of exact solutions of nonlinear differential equations. Two basic ideas are in the focus of our approach. One of them is to use the general solutions of the simplest nonlinear differential equations. Another idea is to take into consideration all possible singularities of the studied equation. Applications of our approach to search for exact solutions of nonlinear differential equations is discussed in detail. The method is used to investigate the exact solutions of the Kuramoto-Sivashinsky equation and the equation for the description of nonlinear waves in a convective fluid. New exact solitary and periodic waves of these equations are given.

MSC 2000:: *35C05 Solutions of PDE in closed form
35Q53 KdV-like equations

Keywords: Kuramoto-Sivashinsky equation; solitary waves; periodic waves

Cited in: Zbl 1200.65056

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