115 research outputs found
Travelling solitons in the parametrically driven nonlinear Schroedinger equation
We show that the parametrically driven nonlinear Schroedinger equation has
wide classes of travelling soliton solutions, some of which are stable. For
small driving strengths nonpropogating and moving solitons co-exist while
strongly forced solitons can only be stably when moving sufficiently fast.Comment: The paper is available as the JINR preprint E17-2000-147(Dubna,
Russia) and the preprint of the Max-Planck Institute for the Complex Systems
mpipks/0009011, Dresden, Germany. It was submitted to Physical Review
Two and three-dimensional oscillons in nonlinear Faraday resonance
We study 2D and 3D localised oscillating patterns in a simple model system
exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is
shown to have exact soliton solutions which are found to be always unstable in
3D. On the contrary, the 2D solitons are shown to be stable in a certain
parameter range; hence the damping and parametric driving are capable of
suppressing the nonlinear blowup and dispersive decay of solitons in two
dimensions. The negative feedback loop occurs via the enslaving of the
soliton's phase, coupled to the driver, to its amplitude and width.Comment: 4 pages; 1 figur
Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation
It is well known that pulse-like solutions of the cubic complex
Ginzburg-Landau equation are unstable but can be stabilised by the addition of
quintic terms. In this paper we explore an alternative mechanism where the role
of the stabilising agent is played by the parametric driver. Our analysis is
based on the numerical continuation of solutions in one of the parameters of
the Ginzburg-Landau equation (the diffusion coefficient ), starting from the
nonlinear Schr\"odinger limit (for which ). The continuation generates,
recursively, a sequence of coexisting stable solutions with increasing number
of humps. The sequence "converges" to a long pulse which can be interpreted as
a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR
Complexes of stationary domain walls in the resonantly forced Ginsburg-Landau equation
The parametrically driven Ginsburg-Landau equation has well-known stationary
solutions -- the so-called Bloch and Neel, or Ising, walls. In this paper, we
construct an explicit stationary solution describing a bound state of two
walls. We also demonstrate that stationary complexes of more than two walls do
not exist.Comment: 10 pages, 2 figures, to appear in Physical Review
Noncoaxial multivortices in the complex sine-Gordon theory on the plane
We construct explicit multivortex solutions for the complex sine-Gordon
equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the
previously found (coaxial) multivortices, the new solutions comprise single
vortices placed at arbitrary positions (but confined within a finite part of
the plane.) All multivortices, including the single vortex, have an infinite
number of parameters. We also show that, in contrast to the coaxial complex
sine-Gordon multivortices, the axially-symmetric solutions of the
Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) {\it do not}
belong to a broader family of noncoaxial multivortex configurations.Comment: 40 pages, 7 figures in colou
Fragmentation of Nuclei at Intermediate and High Energies in Modified Cascade Model
The process of nuclear multifragmentation has been implemented, together with
evaporation and fission channels of the disintegration of excited remnants in
nucleus-nucleus collisions using percolation theory and the intranuclear
cascade model. Colliding nuclei are treated as face--centered--cubic lattices
with nucleons occupying the nodes of the lattice. The site--bond percolation
model is used. The code can be applied for calculation of the fragmentation of
nuclei in spallation and multifragmentation reactions.Comment: 19 pages, 10 figure
Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation
The Gross-Pitaevskii approximation is a long-wavelength theory widely used to
describe a variety of properties of dilute Bose condensates, in particular
trapped alkali gases. We point out that for short-ranged repulsive interactions
this theory fails in dimensions d less than or equal to 2, and we propose the
appropriate low-dimensional modifications. For d=1 we analyze density profiles
in confining potentials, superfluid properties, solitons, and self-similar
solutions.Comment: 4 pages, 3 figure
Cuspons, peakons and regular gap solitons between three dispersion curves
A general wave model with the cubic nonlinearity is introduced to describe a
situation when the linear dispersion relation has three branches, which would
intersect in the absence of linear couplings between the three waves. Actually,
the system contains two waves with a strong linear coupling between them, to
which a third wave is then coupled. This model has two gaps in its linear
spectrum. Realizations of this model can be made in terms of temporal or
spatial evolution of optical fields in, respectively, a planar waveguide or a
bulk-layered medium resembling a photonic-crystal fiber. Another physical
system described by the same model is a set of three internal wave modes in a
density-stratified fluid. A nonlinear analysis is performed for solitons which
have zero velocity in the reference frame in which the group velocity of the
third wave vanishes. Disregarding the self-phase modulation (SPM) term in the
equation for the third wave, we find two coexisting families of solitons:
regular ones, which may be regarded as a smooth deformation of the usual gap
solitons in a two-wave system, and cuspons with a singularity in the first
derivative at their center. Even in the limit when the linear coupling of the
third wave to the first two vanishes, the soliton family remains drastically
different from that in the linearly uncoupled system; in this limit, regular
solitons whose amplitude exceeds a certain critical value are replaced by
peakons. While the regular solitons, cuspons, and peakons are found in an exact
analytical form, their stability is tested numerically, which shows that they
all may be stable. If the SPM terms are retained, we find that there again
coexist two different families of generic stable soliton solutions, namely,
regular ones and peakons.Comment: a latex file with the text and 10 pdf files with figures. Physical
Review E, in pres
Total Cross Section, Inelasticity and Multiplicity Distributions in Proton -- Proton Collisions
Multiparticle production in high energy proton -- proton collisions has been
analysed in the frame of Strongly Correlated Quark Model (SCQM) of the hadron
structure elaborated by the author. It is shown that inelasticity decreases at
high energies and this effect together with the total cross section growth and
the increasing with collision energy the masses of intermediate clusters result
in the violation of KNO -- scaling.Comment: 21 pages, 11 figures, submitted to Yad. Fisik
A system of ODEs for a Perturbation of a Minimal Mass Soliton
We study soliton solutions to a nonlinear Schrodinger equation with a
saturated nonlinearity. Such nonlinearities are known to possess minimal mass
soliton solutions. We consider a small perturbation of a minimal mass soliton,
and identify a system of ODEs similar to those from Comech and Pelinovsky
(2003), which model the behavior of the perturbation for short times. We then
provide numerical evidence that under this system of ODEs there are two
possible dynamical outcomes, which is in accord with the conclusions of
Pelinovsky, Afanasjev, and Kivshar (1996). For initial data which supports a
soliton structure, a generic initial perturbation oscillates around the stable
family of solitons. For initial data which is expected to disperse, the finite
dimensional dynamics follow the unstable portion of the soliton curve.Comment: Minor edit
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