This paper gives a pedagogic review of the envelope formalism for excitation of zonal flows by nonlinear interactions of plasma drift waves or Rossby waves, described equivalently by the Hasegawa–Mima (HM) equation or the quasigeostrophic barotropic potential vorticity equation, respectively. In the plasma case a modified form of the HM equation, which takes into account suppression of the magn...

Martin Centurion, Mason A. Porter, Ye Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and Demetri Psaltis Max Planck Institute for Quantum Optics, 85748 Garching, Germany Department of Physics and Center for the Physics of Information, California Institute of Technology, Pasadena, California 91125, USA Department of Electrical Engineering, California Institute of Technology, Pasadena, California 911...

We report on the detailed experimental determination of the threshold for modulational instability in a photorefractive single-mirror feedback system using a Fourier control technique. Results are compared to analytical predictions and a disagreement for the experimentally significant multiple pattern region is found. Implications for the generation of nonhexagonal two-dimensional patterns are ...

We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction of spatial solitons.

We demonstrate that a weak defocusing Kerr effect in an optical medium with predominantly quadratic [or chi((2))] nonlinear response can eliminate the parametric modulational instability of plane waves, leading to the existence of stable two-wave dark and vortex spatial solitons.