Grid states and nonlinear selection in parametrically excited surface waves

T. Epstein and J. Fineberg

The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

_Received 11 August 2005; published 12 May 2006_

Interacting surface waves, parametrically excited by two commensurate frequencies _Faraday waves_, yield

a rich family of nonlinear states, which result from a variety of three-wave resonant interactions. By perturbing

the system with a third frequency, we selectively favor different nonlinear wave interactions. Where quadratic

nonlinearities are dominant, the only observed patterns correspond to “grid” states. Grid states are superlattices

in which two corotated sets of critical wave vectors are spanned by a sublattice whose basis states are linearly

stable modes. Specific driving phase combinations govern the selection of different grid states.