From power law to Anderson localization in nonlinear Schrödinger equation with nonlinear randomness

Abstract

We study the propagation of coherent waves in a nonlinearly-induced random potential, and find regimes of self-organized criticality and other regimes where the nonlinear equivalent of Anderson localization prevails. The regime of self-organized criticality leads to power-law decay of transport [Phys. Rev. Lett. 121, 233901 (2018)], whereas the second regime exhibits exponential decay.

References in corpus (7)

• Anderson localization and nonlinearity in one dimensional disordered photonic lattices
• Selection of the ground state for nonlinear Schroedinger equations
• Superfluidity versus Anderson localization in a dilute Bose gas
• Semiclassical asymptotics for weakly nonlinear Bloch waves
• Adiabatic theorems for linear and nonlinear Hamiltonians
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Cited by in corpus (4)

• A self-consistent model of the plasma staircase and nonlinear Schrödinger equation with subquadratic power nonlinearity
• Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations
• Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries
• Power-law localization in one-dimensional systems with nonlinear disorder under fixed input conditions