153 research outputs found
Landau-Zener Tunneling of Bose-Einstein Condensates in an Optical Lattice
A theory of the non-symmetric Landau-Zener tunneling of Bose-Einstein
condensates in deep optical lattices is presented. It is shown that periodic
exchange of matter between the bands is described by a set of linearly coupled
nonlinear Schr\"{o}dinger equations. The key role of the modulational
instability in rendering the inter-band transitions irreversible is
highlighted.Comment: 4 pages, 3 figure
Dissipative surface solitons in periodic structures
We report dissipative surface solitons forming at the interface between a
semi-infinite lattice and a homogeneous Kerr medium. The solitons exist due to
balance between amplification in the near-surface lattice channel and
two-photon absorption. The stable dissipative surface solitons exist in both
focusing and defocusing media, when propagation constants of corresponding
states fall into a total semi-infinite and or into one of total finite gaps of
the spectrum (i.e. in a domain where propagation of linear waves is inhibited
for the both media). In a general situation, the surface solitons form when
amplification coefficient exceeds threshold value. When a soliton is formed in
a total finite gap there exists also the upper limit for the linear gain.Comment: 5 pages, 3 figures, to appear in Europhysics Letter
On dissipationless shock waves in a discrete nonlinear Schr\"odinger equation
It is shown that the generalized discrete nonlinear Schr\"odinger equation
can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or
the fifth-order KdV equations, depending on values of the parameters. In
dispersionless limit these equations lead to wave breaking phenomenon for
general enough initial conditions, and, after taking into account small
dispersion effects, result in formation of dissipationless shock waves. The
Whitham theory of modulations of nonlinear waves is used for analytical
description of such waves.Comment: 15 pages, 9 figure
Shock waves in one-dimensional Heisenberg ferromagnets
We use SU(2) coherent state path integral formulation with the stationary
phase approximation to investigate, both analytically and numerically, the
existence of shock waves in the one- dimensional Heisenberg ferromagnets with
anisotropic exchange interaction. As a result we show the existence of shock
waves of two types,"bright" and "dark", which can be interpreted as moving
magnetic domains.Comment: 10 pages, with 3 ps figure
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