Dispersion relation around the kink solution of the Cahn-Hilliard equation

The dispersion relation of the long-wavelength fluctuations of an interface exhibited by the Cahn-Hilliard equation is studied analytically and numerically. The expected asymptotic dispersion relation ω∼${\mathit{k}}^3$ is demonstrated. Further, using a well-defined microscopic length scale ξ, the dispersion relation is numerically found to have a nearly universal form ω/${\mathit{k}}^3$=(1/ξ)Ω(kξ) for a wide variety of potentials.