Abstract

The propagation of interfaces between different equilibria exhibits a rich dynamics and morphology, where stalactites and snowflakes are paradigmatic examples. Here, we study the stability features of flat fronts within the framework of the subcritical Newell-Whitehead-Segel equation. This universal amplitude equation accounts for stripe formation near a weakly inverted bifurcation and front solutions between a uniform state and a stripes pattern. We show that these domain walls are linearly unstable. The flat interface develops a transversal pattern-like structure with a well defined wavelength, later on, the transversal structure becomes a zigzag structure: This zigzag displays a coarsening dynamics, with the consequent growing of the wavelength. We study the relation between this interface instability and those exhibited by the interface connecting a stripes pattern with a uniform state in the theoretical framework of subcritical Swift-Hohenberg equation. A transversally flat wall domain could be stabilized by the pinning effect, this dynamical behavior is lost in the subcritical Newell-Whitehead-Segel approach. However, this flat interface is a metastable state and in the presence of noise the system develops a similar behavior to the subcritical Newell-Whitehead-Segel equation.