Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2001-07-31
Nonlinear Sciences
Pattern Formation and Solitons
The paper contains 34 pages and 53 figures and provides an extensive review of both the theoretical and experimental work pefo
Scientific paper
10.1103/PhysRevE.65.036224
We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different 3--wave resonant interactions. They occur either as symmetry--breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two primary unstable modes generated by the two forcing frequencies. A coherent picture of these states together with the phase space in which they appear is presented. In addition, we describe a number of new superlattice states generated by 4--wave interactions that arise when symmetry constraints rule out 3--wave resonances.
Arbell H.
Fineberg Jay
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