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Solitary wave solutions to the Kuramoto-Sivashinsky equation by means of the homotopy analysis method. (English) Zbl 1173.35646

Summary: The homotopy analysis method is used to find a family of solitary solutions of the Kuramoto-Sivashinsky equation. This approximate solution, which is obtained as a series of exponentials, has a reasonable residual error. The homotopy analysis method contains the auxiliary parameter \(\hbar\), which provides us with a simple way to adjust and control the convergence region of series solution. This method is reliable and manageable.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C10 Series solutions to PDEs
35A35 Theoretical approximation in context of PDEs
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