2,102 research outputs found
Bilinear structure and Schlesinger transforms of the -P and -P equations
We show that the recently derived (-) discrete form of the Painlev\'e VI
equation can be related to the discrete P, in particular if one
uses the full freedom in the implementation of the singularity confinement
criterion. This observation is used here in order to derive the bilinear forms
and the Schlesinger transformations of both -P and -P.Comment: 10 pages, Plain Te
Observability of Dark Matter Substructure with Pulsar Timing Correlations
Dark matter substructure on small scales is currently weakly constrained, and
its study may shed light on the nature of the dark matter. In this work we
study the gravitational effects of dark matter substructure on measured pulsar
phases in pulsar timing arrays (PTAs). Due to the stability of pulse phases
observed over several years, dark matter substructure around the Earth-pulsar
system can imprint discernible signatures in gravitational Doppler and Shapiro
delays. We compute pulsar phase correlations induced by general dark matter
substructure, and project constraints for a few models such as monochromatic
primordial black holes (PBHs), and Cold Dark Matter (CDM)-like NFW subhalos.
This work extends our previous analysis, which focused on static or single
transiting events, to a stochastic analysis of multiple transiting events. We
find that stochastic correlations, in a PTA similar to the Square Kilometer
Array (SKA), are uniquely powerful to constrain subhalos as light as , with concentrations as low as that predicted by standard
CDM.Comment: 45 pages, 12 figure
Do All Integrable Evolution Equations Have the Painlev\'e Property?
We examine whether the Painleve property is necessary for the integrability
of partial differential equations (PDEs). We show that in analogy to what
happens in the case of ordinary differential equations (ODEs) there exists a
class of PDEs, integrable through linearisation, which do not possess the
Painleve property. The same question is addressed in a discrete setting where
we show that there exist linearisable lattice equations which do not possess
the singularity confinement property (again in analogy to the one-dimensional
case).Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Integrable systems without the Painlev\'e property
We examine whether the Painlev\'e property is a necessary condition for the
integrability of nonlinear ordinary differential equations. We show that for a
large class of linearisable systems this is not the case. In the discrete
domain, we investigate whether the singularity confinement property is
satisfied for the discrete analogues of the non-Painlev\'e continuous
linearisable systems. We find that while these discrete systems are themselves
linearisable, they possess nonconfined singularities
Nonintegrability of (2+1)-dimensional continuum isotropic Heisenberg spin system: Painlev\'e analysis
While many integrable spin systems are known to exist in (1+1) and (2+1)
dimensions, the integrability property of the physically important (2+1)
dimensional isotropic Heisenberg ferromagnetic spin system in the continuum
limit has not been investigated in the literature. In this paper, we show
through a careful singularity structure analysis of the underlying nonlinear
evolution equation that the system admits logarithmic type singular manifolds
and so is of non-Painlev\'e type and is expected to be nonintegrable.Comment: 11 pages. to be published in Phys. Lett. A (2006
Riccati Solutions of Discrete Painlev\'e Equations with Weyl Group Symmetry of Type
We present a special solutions of the discrete Painlev\'e equations
associated with , and -surface. These
solutions can be expressed by solutions of linear difference equations. Here
the -surface discrete Painlev\'e equation is the most generic
difference equation, as all discrete Painlev\'e equations can be obtained by
its degeneration limit. These special solutions exist when the parameters of
the discrete Painlev\'e equation satisfy a particular constraint. We consider
that these special functions belong to the hypergeometric family although they
seems to go beyond the known discrete and -discrete hypergeometric
functions. We also discuss the degeneration scheme of these solutions.Comment: 22 page
Pulsar Timing Probes of Primordial Black Holes and Subhalos
Pulsars act as accurate clocks, sensitive to gravitational redshift and
acceleration induced by transiting clumps of matter. We study the sensitivity
of pulsar timing arrays (PTAs) to single transiting compact objects, focusing
on primordial black holes and compact subhalos in the mass range from to well above . We find that the Square Kilometer
Array can constrain such objects to be a subdominant component of the dark
matter over this entire mass range, with sensitivity to a dark matter
sub-component reaching the sub-percent level over significant parts of this
range. We also find that PTAs offer an opportunity to probe substantially less
dense objects than lensing because of the large effective radius over which
such objects can be observed, and we quantify the subhalo concentration
parameters which can be constrained.Comment: 18 pages, 6 figure
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