Perturbations of planar interfaces in Ginzburg-Landau models

Certain dissipative Ginzburg-Landau models predict existence of planar interfaces moving with constant velocity. In most cases the interface solutions are hard to obtain because pertinent evolution equations are nonlinear. We present a systematic perturbative expansion which allows us to compute effects of small terms added to the free energy functional of a soluble model. As an example, we take the exactly soluble model with single order parameter $phi$ and the potential $V_0(phi) = Aphi^2 + B phi^3 + phi^4$, and we perturb it by adding $V_1(phi) = {1/2} epsilon_1 phi^2 partial_i phi partial_i phi + 1/5 epsilon_2 phi^5 + 1/6 epsilon_3 phi^6. $ We discuss the corresponding changes of the velocity of the planar interface.