1D Cahn-Hilliard equation for modulated phase systems

Formation of modulated phase patterns can be modelized by a modified Cahn-Hilliard equation which includes a non local term preventing the formation of macroscopic domains. Using stationnary solutions of the original Cahn-Hilliard equation as analytical ansatzs, we compute the thermodynamically stable period of a 1D modulated phase pattern. We find that the period scales like the power -1/3 of the strength of the long range interactio