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Popular ansatz methods and solitary wave solutions of the Kuramoto-Sivashinsky equation. (English) Zbl 1229.34008
Summary: Some methods to look for exact solutions of nonlinear differential equations are discussed. It is shown that many popular methods are equivalent to each other. Several recent publications with “new” solitary wave solutions for the Kuramoto-Sivashinsky equation are analyzed. We demonstrate that all these solutions coincide with the known ones.
MSC:
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
35Q53KdV-like (Korteweg-de Vries) equations
34M05Entire and meromorphic solutions (ODE)
35C05Solutions of PDE in closed form