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Simplest equation method to look for exact solutions of nonlinear differential equations. (English) Zbl 1069.35018

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:

35C05 Solutions to PDEs in closed form
35Q53 KdV equations (Korteweg-de Vries equations)
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