11 research outputs found
Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates with attraction
We present spatially localized nonrotating and rotating (azimuthon)
multisolitons in the two-dimensional (2D) ("pancake-shaped configuration")
Bose-Einstein condensate (BEC) with attractive interaction. By means of a
linear stability analysis, we investigate the stability of these structures and
show that rotating dipole solitons are stable provided that the number of atoms
is small enough. The results were confirmed by direct numerical simulations of
the 2D Gross-Pitaevskii equation.Comment: 4 pages, 4 figure
Two-dimensional nonlinear vector states in Bose-Einstein condensates
Two-dimensional (2D) vector matter waves in the form of soliton-vortex and
vortex-vortex pairs are investigated for the case of attractive intracomponent
interaction in two-component Bose-Einstein condensates. Both attractive and
repulsive intercomponent interactions are considered. By means of a linear
stability analysis we show that soliton-vortex pairs can be stable in some
regions of parameters while vortex-vortex pairs turn out to be always unstable.
The results are confirmed by direct numerical simulations of the 2D coupled
Gross-Pitaevskii equations.Comment: 6 pages, 9 figure
The Darboux transformation of the derivative nonlinear Schr\"odinger equation
The n-fold Darboux transformation (DT) is a 2\times2 matrix for the
Kaup-Newell (KN) system. In this paper,each element of this matrix is expressed
by a ratio of determinant and determinant of
eigenfunctions. Using these formulae, the expressions of the and
in KN system are generated by n-fold DT. Further, under the reduction
condition, the rogue wave,rational traveling solution, dark soliton, bright
soliton, breather solution, periodic solution of the derivative nonlinear
Schr\"odinger(DNLS) equation are given explicitly by different seed solutions.
In particular, the rogue wave and rational traveling solution are two kinds of
new solutions. The complete classification of these solutions generated by
one-fold DT is given in the table on page.Comment: 21 papge, 10 figure
An instability criterion for nonlinear standing waves on nonzero backgrounds
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity
is considered. As an example, a system with a spatially varying coefficient of
the nonlinear term is studied. The nonlinearity is chosen to be repelling
except on a finite interval. Localized standing wave solutions on a non-zero
background, e.g., dark solitons trapped by the inhomogeneity, are identified
and studied. A novel instability criterion for such states is established
through a topological argument. This allows instability to be determined
quickly in many cases by considering simple geometric properties of the
standing waves as viewed in the composite phase plane. Numerical calculations
accompany the analytical results.Comment: 20 pages, 11 figure