Abstract
On the basis of topological arguments, it is shown that phase jump lines arise in two-dimensional cellular patterns. A phase jump line either ends at a phase singularity with a half-integer topological charge or it has no endpoints. As a simple model equation which exhibits such lines, a set of amplitude equations describing resonant interaction between two modes with wave numbers k and 2k is considered. Numerical simulations of the model equations show that these lines are spontaneously formed in ordering process of cellular structures.
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