Perturbations of planar interfaces in Ginzburg-Landau models

Original · EN

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 V₀(ϕ) = Aϕ² + B ϕ³ + ϕ⁴, and we perturb it by adding V₁(ϕ) = 1/2 ε₁ ϕ² ∂ᵢ ϕ∂ᵢ ϕ+ 1/5 ε₂ ϕ⁵ + 1/6 ε₃ ϕ⁶. We discuss the corresponding changes of the velocity of the planar interface.