Enhanced localization of waves in one-dimensional random media due to nonlinearity: Fixed input case

Wave Propagation and Localization in a Complex Random Potential with Power-law Correlations: A Numerical Study

“…Therefore, we developed a reliable theoretical method for solving Eqs. (4) and (5) numerically in the situation where the incident wave intensity, 2 0 , r is fixed [43][44][45]. In particular, we first assume that t is a certain positive real number.…”

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

“…(1), when Ψ(x, t) = e −iωt ψ(x) (2) relates to the Anderson localization [1,2] of the stationary states of the NLSE. Another important task is wave propagation in nonlinear media [3][4][5][6][7][8][9][10][11], where the problem of spreading of wave packets and transmission are not simply related [6,7,12,13], in contrast with the linear case. This problem is relevant for experiments in nonlinear optics, for example disordered photonic lattices [14,15], where Anderson localization was found in presence of nonlinear effects.…”

Mobility Edges in One-dimensional Disordered Aharonov-Bohm Rings

“…Anderson localization of quantum particles and classical waves in a random potential has been studied extensively for a long time [1][2][3][4][5]. Despite of a huge amount of research into this field, there still remain many unsolved problems and suprising results are being reported [6][7][8]. It has been widely known that in one and two dimensions, noninteracting quantum particles and classical waves are usually localized even in the presence of arbitrarily weak randomness [3,4].…”