Self-organization processes in continuous media

Abstract

This review considers the dynamical behaviour of dissipative continuous media which can be described by nonlinear partial differential equations having more than two non-trivial conserved quantities in the absence of dissipation. Such a medium often exhibits a spectral condensation of a certain physical quantity to a specific wavenumber region resulting in the formation of an ordered structure, even when starting from an initially turbulent state or one driven by a stochastic field. Examples discussed here include two-dimensional incompressible fluids, two-and three-dimensional magnetohydrodynamic fluids, the atmospheres of rotating planets, the electrostatic potential in inhomogeneous magnetized plasmas, and the solition gas as described by the Korteweg-de Vries equation. The relationship between the onset of chaos and self-organization in a soliton system, as well as in some localized vortex solutions, is also discussed.