Discrete nonlinear Schrodinger equation with defects
Year: 2003
Authors: Trombettoni A., Smerzi A., Bishop A.R.
Autors Affiliation: Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA; Los Alamos Natl Lab, Ctr Nonlinear Studies, Los Alamos, NM 87545 USA; Univ Perugia, Dipartimento Fis, I-06123 Perugia, Italy; Univ Perugia, Sez INFN, I-06123 Perugia, Italy.
Abstract: We investigate the dynamical properties of the one-dimensional discrete nonlinear Schrodinger equation (DNLS) with periodic boundary conditions and with an arbitrary distribution of on-site defects. We study the propagation of a traveling plane wave with momentum k: the dynamics in Fourier space mainly involves two localized states with momenta +/-k (corresponding to a transmitted and a reflected wave). Within a two-mode ansatz in Fourier space, the dynamics of the system maps on a nonrigid pendulum Hamiltonian. The several analytically predicted (and numerically confirmed) regimes include states with a vanishing time average of the rotational states (implying complete reflections and refocusing of the incident wave), oscillations around fixed points (corresponding to quasi-stationary states), and, above a critical value of the nonlinearity, self-trapped states (with the wave traveling almost undisturbed through the impurity). We generalize this treatment to the case of several traveling waves and time-dependent defects. The validity of the two-mode ansatz and the continuum limit of the DNLS are discussed.
Journal/Review: PHYSICAL REVIEW E
Volume: 67 (1) Pages from: 16607-1 to: 16607-11
KeyWords: Bose-einstein Condensation; Solitons; DynamicsDOI: 10.1103/PhysRevE.67.016607Citations: 24data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)