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 $\varphi$ and the potential $V_0(\varphi )=A{\varphi }^2+B{\varphi }^3+{\varphi }^4$, and we perturb it by adding $V_1(\varphi )=1/2{\epsilon }_1{\varphi }^2{\partial }_i\varphi {\partial }_i\varphi +1/5{\epsilon }_2{\varphi }^5+1/6{\epsilon }_3{\varphi }^6.$ We discuss the corresponding changes of the velocity of the planar interface.

13 pages, no figures, LaTeX2e