250 research outputs found
Condition for convective instability of dark solitons
Simple derivation of the condition for the transition point from absolute
instability of plane dark solitons to their convective instability is
suggested. It is shown that unstable wave packet expands with velocity equal to
the minimal group velocity of the disturbance waves propagating along a dark
soliton. The growth rate of the length of dark solitons generated by the flow
of Bose-Einstein condensate past an obstacle is estimated. Analytical theory is
confirmed by the results of numerical simulations
On Whitham theory for perturbed integrable equations
Whitham theory of modulations is developed for periodic waves described by
nonlinear wave equations integrable by the inverse scattering transform method
associated with matrix or second order scalar spectral problems. The
theory is illustrated by derivation of the Whitham equations for perturbed
Korteweg-de Vries equation and nonlinear Schr\"odinger equation with linear
damping.Comment: 17 pages, no figure
Estimating the parameters of the Sgr A* black hole
The measurement of relativistic effects around the galactic center may allow
in the near future to strongly constrain the parameters of the supermassive
black hole likely present at the galactic center (Sgr A*). As a by-product of
these measurements it would be possible to severely constrain, in addition,
also the parameters of the mass-density distributions of both the innermost
star cluster and the dark matter clump around the galactic center.Comment: Accepted for publication on General Relativity and Gravitation, 2010.
11 Pages, 1 Figur
On the calculation of finite-gap solutions of the KdV equation
A simple and general approach for calculating the elliptic finite-gap
solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is
based on the use of the finite-gap equations and the general representation of
these solutions in the form of rational functions of the elliptic Weierstrass
function. The calculation of initial elliptic finite-gap solutions is reduced
to the solution of the finite-band equations with respect to the parameters of
the representation. The time evolution of these solutions is described via the
dynamic equations of their poles, integrated with the help of the finite-gap
equations. The proposed approach is applied by calculating the elliptic 1-, 2-
and 3-gap solutions of the KdV equations
Generalized Action Invariants for Drift Waves-Zonal Flow Systems
Generalized action invariants are identified for various models of drift wave turbulence in the presence of the mean shear flow. It is shown that the wave kinetic equation describing the interaction of the small scale turbulence and large scale shear flow can be naturally written in terms of these invariants. Unlike the wave energy, which is conserved as a sum of small- and large- scale components, the generalized action invariant is shown to correspond to a quantity which is conserved for the small scale component alone. This invariant can be used to construct canonical variables leading to a different definition of the wave action (as compared to the case without shear flow). It is suggested that these new canonical action variables form a natural basis for the description of the drift wave turbulence with a mean shear flow
Partonic energy loss in ultrarelativistic heavy ion collisions: jet suppression versus jet fragmentation softening
We discuss the modification of a jet fragmentation function due to
medium-induced partonic energy loss in context of leading particle observables
in ultrarelativistic nucleus-nucleus interactions. We also analyze the relation
between in-medium softening jet fragmentation function and suppression of the
jet rates due to energy loss outside the jet cone. The predicted
anti-correlation between two effects allows to probe a fraction of partonic
energy loss carried out of the jet cone and truly lost to the jet.Comment: LaTeX, 12 pages including 2 eps-figure
On generating functions in the AKNS hierarchy
It is shown that the self-induced transparency equations can be interpreted
as a generating function for as positive so negative flows in the AKNS
hierarchy. Mutual commutativity of these flows leads to other hierarchies of
integrable equations. In particular, it is shown that stimulated Raman
scattering equations generate the hierarchy of flows which include the
Heisenberg model equations. This observation reveals some new relationships
between known integrable equations and permits one to construct their new
physically important combinations. Reductions of the AKNS hierarchy to ones
with complex conjugate and real dependent variables are also discussed and the
corresponding generating functions of positive and negative flows are found.
Generating function of Whitham modulation equations in the AKNS hierarchy is
obtained.Comment: 11 pages, no figure
Multimode solutions of first-order elliptic quasilinear systems obtained from Riemann invariants
Two new approaches to solving first-order quasilinear elliptic systems of
PDEs in many dimensions are proposed. The first method is based on an analysis
of multimode solutions expressible in terms of Riemann invariants, based on
links between two techniques, that of the symmetry reduction method and of the
generalized method of characteristics. A variant of the conditional symmetry
method for constructing this type of solution is proposed. A specific feature
of that approach is an algebraic-geometric point of view, which allows the
introduction of specific first-order side conditions consistent with the
original system of PDEs, leading to a generalization of the Riemann invariant
method for solving elliptic homogeneous systems of PDEs. A further
generalization of the Riemann invariants method to the case of inhomogeneous
systems, based on the introduction of specific rotation matrices, enables us to
weaken the integrability condition. It allows us to establish a connection
between the structure of the set of integral elements and the possibility of
constructing specific classes of simple mode solutions. These theoretical
considerations are illustrated by the examples of an ideal plastic flow in its
elliptic region and a system describing a nonlinear interaction of waves and
particles. Several new classes of solutions are obtained in explicit form,
including the general integral for the latter system of equations
Profiles of emission lines generated by rings orbiting braneworld Kerr black holes
In the framework of the braneworld models, rotating black holes can be
described by the Kerr metric with a tidal charge representing the influence of
the non-local gravitational (tidal) effects of the bulk space Weyl tensor onto
the black hole spacetime. We study the influence of the tidal charge onto
profiled spectral lines generated by radiating tori orbiting in vicinity of a
rotating black hole. We show that with lowering the negative tidal charge of
the black hole, the profiled line becomes to be flatter and wider keeping their
standard character with flux stronger at the blue edge of the profiled line.
The extension of the line grows with radius falling and inclination angle
growing. With growing inclination angle a small hump appears in the profiled
lines due to the strong lensing effect of photons coming from regions behind
the black hole. For positive tidal charge () and high inclination angles
two small humps appear in the profiled lines close to the red and blue edge of
the lines due to the strong lensing effect. We can conclude that for all values
of , the strongest effect on the profiled lines shape (extension) is caused
by the changes of the inclination angle.Comment: Accepted by General Relativity and Gravitatio
Phenomenology of Jet Quenching in Heavy Ion Collisions
We derive an analytical expression for the quenching factor in the strong
quenching limit where the spectrum of hard partons is dominated by
surface emission. We explore the phenomenological consequences of different
scaling laws for the energy loss and calculate the additional suppression of
the away-side jet.Comment: Substantially modified manuscrip
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