108 research outputs found
Stability of multi-parameter solitons: Asymptotic approach
General asymptotic approach to the stability problem of multi-parameter
solitons in Hamiltonian systems has been developed. It has been shown that asymptotic study of the
soliton stability can be reduced to the calculation of a certain sequence of
the determinants, where the famous determinant of the matrix consisting from
the derivatives of the system invariants with respect to the soliton parameters
is just the first in the series. The presented approach gives first analytical
criterion for the oscillatory instability and also predicts novel stationary
instability. Higher order approximations allow to calculate corresponding
eigenvalues with arbitrary accuracy.Comment: to appear in Physica
Instabilities of vortices in a binary mixture of trapped Bose-Einstein condensates: Role of excitations with positive and negative energies
Correspondence between frequency and energy spectra and biorthogonality
conditions for the excitations of Bose-Einstein condensates described by
Gross-Pitaevskii model have been derived selfconsistently revealing several
novel aspects originating in nonselfadjoitness of the Bogoliubov operator. It
has been demonstrated that frequency resonances of the excitations with
positive and negative energies can lead to their mutual annihilation and
appearance of the collective modes with complex frequencies and zero energies.
Conditions for the avoided crossing of energy levels have also been discussed.
General theory has been verified both numerically and analytically in the weak
interaction limit considering an example of vortices in a binary mixture of
condensates. Growth of excitations with complex frequencies leads to spiraling
of the unit and double vortices out of the condensate center to its periphery
and to splitting of the double and higher order vortices to the unit ones.Comment: Physical Review A (January, 2001). Version 3 differs dramatically
from v1 and v2 and contains significant amount of qualitatively new materia
Clusters of cavity solitons bounded by conical radiation
We introduce a new class of self-sustained states, which may exist as single
solitons or form multisoliton clusters, in driven passive cylindrical
microresonators. Remarkably, such states are stabilized by the radiation they
emit, which strongly breaks spatial symmetry and leads to the appearance of
long polychromatic conical tails. The latter induce long-range soliton
interactions that make possible the formation of clusters, which can be stable
if their spatial arrangement is non-collinear with the soliton rotation
direction in the microcavity. The clusters are intrinsically two-dimensional
and, also, spatially rich. The mechanism behind the formation of the clusters
is explained using soliton clustering theory. Our results bring fundamental
understanding of a new class of multidimensional cavity solitons and may lead
to the development of monolithic multi-soliton sources.Comment: 12 pages, 9 figures, to appear in Physical Review Letter
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