Anderson localization in the quintic nonlinear Schr\"odinger equation
A. T. Avelar, W. B. Cardoso
TL;DR
This paper investigates how quintic nonlinearity affects Anderson localization in the nonlinear Schrödinger equation with disorder, revealing a cutoff condition for localization depending on nonlinearity strength and disorder amplitude.
Contribution
It demonstrates that Anderson localization in the quintic nonlinear Schrödinger equation occurs only below a certain nonlinearity threshold, which depends on the disorder strength.
Findings
Localization requires a cutoff on the quintic nonlinearity parameter.
The cutoff value depends on the amplitude of the random potential.
Nonlinearity influences the persistence of Anderson localization.
Abstract
In the present paper we consider the quintic defocusing nonlinear Schr\"odinger equation in presence of a disordered random potential and we analyze the effects of the quintic nonlinearity on the Anderson localization of the solution. The main result shows that Anderson localization requires a cutoff on the value of the parameter which controls the quintic nonlinearity, with the cutoff depending on the amplitude of the random potential.
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Taxonomy
TopicsNonlinear Photonic Systems · Advanced Mathematical Physics Problems · Numerical methods in inverse problems