Self-organization processes in continuous media

Abstract

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.