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.
Bibliographical noteFunding Information:
D. E. thanks the financial support of Fondecyt, Chile project 1211251 . MGC thanks for the financial support of ANID-Millenium Science Initiative Program, Chile - ICN17_012 (MIRO) and FONDECYT, Chile Project No. 1210353 .
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Daniel Escaff reports financial support was provided by Fondecyt (project 1211251). Marcel G. Clerc reports financial support was provided by ANID- Millenium Science Initiative Program-ICN17 012 (MIRO) and FONDECYT Project No. 1210353.
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- Pattern formation