57 research outputs found
Solution of the dispersionless Hirota equations
The dispersionless differential Fay identity is shown to be equivalent to a
kernel expansion providing a universal algebraic characterization and solution
of the dispersionless Hirota equations. Some calculations based on D-bar data
of the action are also indicated.Comment: Late
On the water-bag model of dispersionless KP hierarchy
We investigate the bi-Hamiltonian structure of the waterbag model of dKP for
two component case. One can establish the third-order and first-order
Hamiltonian operator associated with the waterbag model. Also, the dispersive
corrections are discussed.Comment: 19 page
Coisotropic deformations of associative algebras and dispersionless integrable hierarchies
The paper is an inquiry of the algebraic foundations of the theory of
dispersionless integrable hierarchies, like the dispersionless KP and modified
KP hierarchies and the universal Whitham's hierarchy of genus zero. It stands
out for the idea of interpreting these hierarchies as equations of coisotropic
deformations for the structure constants of certain associative algebras. It
discusses the link between the structure constants and the Hirota's tau
function, and shows that the dispersionless Hirota's bilinear equations are,
within this approach, a way of writing the associativity conditions for the
structure constants in terms of the tau function. It also suggests a simple
interpretation of the algebro-geometric construction of the universal Whitham's
equations of genus zero due to Krichever.Comment: minor misprints correcte
Group-invariant solutions of a nonlinear acoustics model
Based on a recent classification of subalgebras of the symmetry algebra of
the Zabolotskaya-Khokhlov equation, all similarity reductions of this equation
into ordinary differential equations are obtained. Large classes of
group-invariant solutions of the equation are also determined, and some
properties of the reduced equations and exact solutions are discussed.Comment: 14 page
Perturbations of Gauss-Bonnet Black Strings in Codimension-2 Braneworlds
We derive the Lichnerowicz equation in the presence of the Gauss-Bonnet term.
Using the modified Lichnerowicz equation we study the metric perturbations of
Gauss-Bonnet black strings in Codimension-2 Braneworlds.Comment: 26 pages, no figures, clarifying comments and one reference added, to
be published in JHE
Geometry and cosmological perturbations in the bulk inflaton model
We consider a braneworld inflation model driven by the dynamics of a scalar
field living in the 5-dimensional bulk, the so-called ``bulk inflaton model'',
and investigate the geometry in the bulk and large scale cosmological
perturbations on the brane. The bulk gravitational effects on the brane are
described by a projection of the 5-dimensional Weyl tensor, which we denote by
. Focusing on a tachionic potential model, we take a perturbative
approach in the anti-de Sitter (AdS) background with a single de Sitter
brane. We first formulate the evolution equations for in the bulk.
Next, applying them to the case of a spatially homogeneous brane, we obtain two
different integral expressions for . One of them reduces to the
expression obtained previously when evaluated on the brane. The other is a new
expression that may be useful for analyzing the bulk geometry. Then we consider
superhorizon scale cosmological perturbations and evaluate the bulk effects
onto the brane. In the limit , where is the Hubble parameter
on the brane and is the bulk curvature radius, we find that the
effective theory on the brane is identical to the 4-dimensional Einstein-scalar
theory with a simple rescaling of the potential even under the presence of
inhomogeneities. % atleast on super-Hubble horizon scales. In particular, it is
found that the anticipated non-trivial bulk effect due to the spatially
anisotropic part of may appear only at %second order in the low
energy expansion, i.e., at .Comment: 21 pages including 6 pages for several appendixes, no figure
Supersymmetric Intersecting Branes on the Waves
We construct a general family of supersymmetric solutions in time- and
space-dependent wave backgrounds in general supergravity theories describing
single and intersecting p-branes embedded into time-dependent dilaton-gravity
plane waves of an arbitrary (isotropic) profile, with the brane world-volume
aligned parallel to the propagation direction of the wave. We discuss how many
degrees of freedom we have in the solutions. We also propose that these
solutions can be used to describe higher-dimensional time-dependent "black
holes", and discuss their property briefly.Comment: 12 pages, LaTe
S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies
We introduce an S-function formulation for the recently found r-th
dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also
a connection of these -functions with the Orlov functions of the
hierarchies. Then, we discuss a reduction scheme for the hierarchies that
together with the -function formulation leads to hodograph systems for the
associated solutions. We consider also the connection of these reductions with
those of the dispersionless KP hierarchy and with hydrodynamic type systems. In
particular, for the 1-component and 2-component reduction we derive, for both
hierarchies, ample sets of examples of explicit solutions.Comment: 35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel
package
Small localized black holes in a braneworld: Formulation and numerical method
No realistic black holes localized on a 3-brane in the Randall-Sundrum
infinite braneworld have been found so far. The problem of finding a static
black hole solution is reduced to a boundary value problem. We solve it by
means of a numerical method, and show numerical examples of a localized black
hole whose horizon radius is small compared to the bulk curvature scale. The
sequence of small localized black holes exhibits a smooth transition from a
five-dimensional Schwarzschild black hole, which is a solution in the limit of
small horizon radius. The localized black hole tends to flatten as its horizon
radius increases. However, it becomes difficult to find black hole solutions as
its horizon radius increases.Comment: RevTeX, 13 pages, 6 figures, references corrected, typos corrected;
to appear in Phys.Rev.
On Brane World Cosmological Perturbations
We discuss the scalar cosmological perturbations in a 3-brane world with a 5D
bulk. We first show explicitly how the effective perturbed Einstein's equations
on the brane (involving the Weyl fluid) are encoded into Mukohyama's master
equation. We give the relation between Mukohyama's master variable and the
perturbations of the Weyl fluid, we also discuss the relation between the
former and the perturbations of matter and induced metric on the brane. We show
that one can obtain a boundary condition on the brane for the master equation
solely expressible in term of the master variable, in the case of a perfect
fluid with adiabatic perturbations on a Randall-Sundrum (RS) or
Dvali-Gabadadze-Porrati (DGP) brane. This provides an easy way to solve
numerically for the evolution of the perturbations as well as should shed light
on the various approximations done in the literature to deal with the Weyl
degrees of freedom.Comment: 36 pages, 1 figur
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