Necessary Conditions for Mode Interactions in Parametrically Excited Waves

T. Epstein and J. Fineberg

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

(Received 25 December 2007; published 3 April 2008)

We study the spatial and temporal structure of nonlinear states formed by parametrically excited waves

on a fluid surface (Faraday instability), in a highly dissipative regime. Short-time dynamics reveal that 3-

wave interactions between different spatial modes are only observed when the modesí peak values occur

simultaneously. The temporal structure of each mode is functionally described by the Hillís equation and

is unaffected by which nonlinear interaction is dominant.