## 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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### References:

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