1994/01/24 by David Raitt, Raitt, David, Hermann Riecke +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.patt-sol/9401004
openalex publication_date 1994/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Domain walls between spatially periodic patterns with different wave numbers, can arise in pattern-forming systems with a neutral curve that has a double minimum. Within the framework of the phase equation, the interaction of such walls is purely attractive. Thus, they annihilate each other and, if the total phase is not conserved, the final state will be periodic with a single wave number. Here we study the stability of arrays of domain walls (domain structures) in a fourth-order Ginzburg-Landau equation. We find a discrete set of domain structures which differ in the quantized lengths of the domains. They are stable even without phase conservation, as, for instance, in the presence of a subcritical ramp in the control parameter. We attribute this to the spatially oscillatory behavior of the wave number which should lead to an oscillatory interaction between the domain walls. These results are expected to shed also some light on the stability of two-dimensional zig-zag structures.