On wave structures described by the generalized Kuramoto-Sivashinsky equation

The generalized Kuramoto-Sivashinsky equation is considered. The Painlevé test is applied for studying this equation. It is shown that the generalized Kuramoto-Sivashinsky equation does not pass the Painlevé test but has the expansion of the general solution in the Laurent series. As consequence the equation can have some exact solutions at additional conditions on the parameters of equation. Solitary wave and elliptic solutions of the generalized Kuramoto-Sivashinsky equation are found by means of expansion for solution in the Laurent series. It is shown that solutions obtained describe some structures in the medium with the dissipation and instability.