Defects in Semilinear Wave Equations and Timelike Minimal Surfaces in Minkowski Space

We study semilinear wave equations with Ginzburg-Landau type nonlinearities multiplied by a factor ε, where ε > 0 is a small parameter. We prove that for suitable initial data, solutions exhibit energy concentration sets that evolve approximately via the equation for timelike Minkowski minimal surfaces, as long as the minimal surface remains smooth. This gives a proof of predictions made, on the basis of formal asymptotics and other heuristic arguments, by Neu [32], as well as by cosmologists studying cosmic strings and domain walls. September 18, 2009