Περίληψη:
We demonstrate a possibility to generate localized states in effectively
one-dimensional Bose-Einstein condensates with a negative scattering
length in the form of a dark soliton in the presence of an optical
lattice (OL) and/or a parabolic magnetic trap. We connect such
structures with twisted localized modes (TLMs) that were previously
found in the discrete nonlinear Schrodinger equation. Families of these
structures are found as functions of the OL strength, tightness of the
magnetic trap and chemical potential, and their stability regions are
identified. Stable bound states of two TLMs are also found. In the case
when the TLMs are unstable, their evolution is investigated by means of
direct simulations, demonstrating that they transform into
large-amplitude fundamental solitons. An analytical approach is also
developed, showing that two or several fundamental solitons, with the
phase shift p between adjacent ones, may form stable bound states, with
parameters quite close to those of the TLMs revealed by simulations. TLM
structures are also found numerically and explained analytically in the
case when the OL is absent, the condensate being confined only by the
magnetic trap.
Συγγραφείς:
Kevrekidis, PG
Frantzeskakis, DJ
Malomed, BA
Bishop, AR and
Kevrekidis, IG
