Nonlinear wave-packet dynamics in a disordered medium

Abstract

In this article we develop an effective theory of pulse propagation in a nonlinear and disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as "locked explosion" and "diffusive" collapse. In this sense the equation can serve as a paradigmatic model, that can be applied to such distinct physical systems as laser beams propagating in disordered photonic crystals or Bose-Einstein condensates expanding in a disordered environment.

References in corpus (4)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Delocalization induced by nonlinearity in systems with disorder
• Expansion of a Bose-Einstein Condensate in the Presence of Disorder
• Coherent backscattering of Bose-Einstein condensates in two-dimensional disorder potentials

Cited by in corpus (14)

• Cold atoms in the presence of disorder
• How nonlinear interactions challenge the three-dimensional Anderson transition
• Energy Spreading in Strongly Nonlinear Disordered Lattices
• Quantum diffusion with disorder, noise and interaction
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Thermalization of matter waves in speckle potentials
• Fokker-Planck equation for transport of wave packets in nonlinear disordered media
• Quench dynamics of a weakly interacting disordered Bose gas in momentum space
• Do nonlinear waves in random media follow nonlinear diffusion equations?
• Effective theory for the propagation of a wave-packet in a disordered and nonlinear medium
• Microscopic scattering theory for interacting bosons in weak random potentials
• Kinetics of the disordered Bose gas with collisions
• A self-consistent theory of localization in nonlinear random media
• Disordered resonant media: Self-induced transparency versus light localization