In this paper we consider stationary solutions to the nonlinear one-dimensional Schrödinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark--Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs when the ratio between the effective nonlinearity strength and the tilt of the external field increases.
Nonlinear Stark--Wannier Equation / Sacchetti, Andrea. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 50:6(2018), pp. 5783-5810. [10.1137/17M113099X]
Nonlinear Stark--Wannier Equation
Andrea Sacchetti
2018
Abstract
In this paper we consider stationary solutions to the nonlinear one-dimensional Schrödinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark--Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs when the ratio between the effective nonlinearity strength and the tilt of the external field increases.
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