Perturbations of planar interfaces in Ginzburg-Landau models

Abstract

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 $ϕ$ and the potential $V_0(ϕ) = Aϕ^2 + B ϕ^3 + ϕ^4$, and we perturb it by adding $V_1(ϕ) = {1/2} ε_1 ϕ^2 \partial_i ϕ\partial_i ϕ+ 1/5 ε_2 ϕ^5 + 1/6 ε_3 ϕ^6. $ We discuss the corresponding changes of the velocity of the planar interface.