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

Abstract

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 \ensuremath{\omega}\ensuremath{\sim}${\mathit{k}}^{3}$ is demonstrated. Further, using a well-defined microscopic length scale \ensuremath{\xi}, the dispersion relation is numerically found to have a nearly universal form \ensuremath{\omega}/${\mathit{k}}^{3}$=(1/\ensuremath{\xi})\ensuremath{\Omega}(k\ensuremath{\xi}) for a wide variety of potentials.