197 research outputs found
Dispersion-managed soliton in a strong dispersion map limit
A dispersion-managed optical system with step-wise periodical variation of
dispersion is studied in a strong dispersion map limit in the framework of
path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by
iterating the path-averaged equation analytically and numerically. An efficient
numerical algorithm for obtaining of DM soliton shape is developed. The
envelope of soliton oscillating tails is found to decay exponentially in time
while the oscillations are described by a quadratic law.Comment: 11 Pages, 3 Figures; Submitted to Optics Letter
Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Pad\'e approximation
Complex analytical structure of Stokes wave for two-dimensional potential
flow of the ideal incompressible fluid with free surface and infinite depth is
analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating
with the constant velocity. Simulations with the quadruple and variable
precisions are performed to find Stokes wave with high accuracy and study the
Stokes wave approaching its limiting form with radians angle on the
crest. A conformal map is used which maps a free fluid surface of Stokes wave
into the real line with fluid domain mapped into the lower complex half-plane.
The Stokes wave is fully characterized by the complex singularities in the
upper complex half-plane. These singularities are addressed by rational
(Pad\'e) interpolation of Stokes wave in the complex plane. Convergence of
Pad\'e approximation to the density of complex poles with the increase of the
numerical precision and subsequent increase of the number of approximating
poles reveals that the only singularities of Stokes wave are branch points
connected by branch cuts. The converging densities are the jumps across the
branch cuts. There is one branch cut per horizontal spatial period of
Stokes wave. Each branch cut extends strictly vertically above the
corresponding crest of Stokes wave up to complex infinity. The lower end of
branch cut is the square-root branch point located at the distance from
the real line corresponding to the fluid surface in conformal variables. The
limiting Stokes wave emerges as the singularity reaches the fluid surface.
Tables of Pad\'e approximation for Stokes waves of different heights are
provided. These tables allow to recover the Stokes wave with the relative
accuracy of at least . The tables use from several poles to about
hundred poles for highly nonlinear Stokes wave with Comment: 38 pages, 9 figures, 4 tables, supplementary material
Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential
We consider dynamics of Bose-Einstein condensates with long-range attractive
interaction proportional to and arbitrary angular dependence. It is
shown exactly that collapse of Bose-Einstein condensate without contact
interactions is possible only for . Case is critical and requires
number of particles to exceed critical value to allow collapse. Critical
collapse in that case is strong one trapping into collapsing region a finite
number of particles.
Case is supercritical with expected weak collapse which traps rapidly
decreasing number of particles during approach to collapse. For
singularity at is not strong enough to allow collapse but attractive
interaction admits stable self-trapping even in absence of external
trapping potential
Static- and dynamical-phase transition in multidimensional voting models on continua
A voting model (or a generalization of the Glauber model at zero temperature)
on a multidimensional lattice is defined as a system composed of a lattice each
site of which is either empty or occupied by a single particle. The reactions
of the system are such that two adjacent sites, one empty the other occupied,
may evolve to a state where both of these sites are either empty or occupied.
The continuum version of this model in a Ddimensional region with boundary is
studied, and two general behaviors of such systems are investigated. The
stationary behavior of the system, and the dominant way of the relaxation of
the system toward its stationary state. Based on the first behavior, the static
phase transition (discontinuous changes in the stationary profiles of the
system) is studied. Based on the second behavior, the dynamical phase
transition (discontinuous changes in the relaxation-times of the system) is
studied. It is shown that the static phase transition is induced by the bulk
reactions only, while the dynamical phase transition is a result of both bulk
reactions and boundary conditions.Comment: 10 pages, LaTeX2
Dispersion-managed soliton in optical fibers with zero average dispersion
The dispersion-managed (DM) optical system with step-wise periodical
variation of dispersion is studied in the framework of path-averaged
Gabitov-Turitsyn equation. The soliton solution is obtained by iterating the
path-averaged equation. The dependence of soliton parameters on dispersion map
strength is investigated together with the oscillating tails of soliton.Comment: 5 pages, 2 figures, to appear in Optics Letters 25, #16 (2000
On the boundary of the dispersion-managed soliton existence
A breathing soliton-like structure in dispersion-managed (DM) optical fiber
system is studied. It is proven that for negative average dispersion the
breathing soliton is forbidden provided that a modulus of average dispersion
exceed a threshold which depends on the soliton amplitude.Comment: LaTeX, 8 pages, to appear in JETP Lett. 72, #3 (2000
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