Physical Sciences and Mathematics Commons^™

Competition Between Generic And Nongeneric Fronts Inenvelope Equations, James A. Powell, A. C. Newell, C. K. R. T. Jones

James A. Powell

Arguments are presented for understanding the selection of the speed and the nature of the fronts that join stable and unstable states on the supercritical side of first-order phase transitions. It is suggested that from compact support, nonpositive-definite initial conditions, observable front behavior occurs only when the asymptotic spatial structure of a trajectory in the Galilean ordinary differential equation (ODE) corresponds to the most unstable temporal mode in the governing partial differential equation (PDE). This selection criterion distinguishes between a "nonlinear" front, which has its origin in the first-order nature of the bifurcation, and a "linear" front. The nonlinear front …