Exact solutions of the Swift–Hohenberg equation with dispersion

The Swift–Hohenberg equation with dispersion is considered. Traveling wave solutions of the Swift–Hohenberg equation with dispersion are presented. The classification of these solutions is given. It is shown that the Swift–Hohenberg equation without dispersion has only stationary meromorphic solution.

► Algorithm for constructing exact solutions is presented.
► We study and classify exact solutions of the Swift–Hohenberg equation with dispersion.
► Exact solutions of the Swift–Hohenberg equation with dispersion are given.