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 $V_0(\phi) = A\phi^2 + B \phi^3 + \phi^4$, 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.