3,052 research outputs found
Cosmic magnetic fields from velocity perturbations in the early Universe
We show, using a covariant and gauge-invariant charged multifluid
perturbation scheme, that velocity perturbations of the matter-dominated dust
Friedmann-Lemaitre-Robertson-Walker (FLRW) model can lead to the generation of
cosmic magnetic fields. Moreover, using cosmic microwave background (CMB)
constraints, it is argued that these fields can reach strengths of between
10^{-28} and 10^{-29} G at the time the dynamo mechanism sets in, making them
plausible seed field candidates.Comment: 11 pages, 1 figure, IOP style, minor changes and typos correcte
Hamiltonians separable in cartesian coordinates and third-order integrals of motion
We present in this article all Hamiltonian systems in E(2) that are separable
in cartesian coordinates and that admit a third-order integral, both in quantum
and in classical mechanics. Many of these superintegrable systems are new, and
it is seen that there exists a relation between quantum superintegrable
potentials, invariant solutions of the Korteweg-De Vries equation and the
Painlev\'e transcendents.Comment: 19 pages, Will be published in J. Math. Phy
New exact fronts for the nonlinear diffusion equation with quintic nonlinearities
We consider travelling wave solutions of the reaction diffusion equation with
quintic nonlinearities . If the parameters
and obey a special relation, then the criterion for the existence of a
strong heteroclinic connection can be expressed in terms of two of these
parameters. If an additional restriction is imposed, explicit front solutions
can be obtained. The approach used can be extended to polynomials whose highest
degree is odd.Comment: Revtex, 5 page
Eguchi-Hanson Solitons in Odd Dimensions
We present a new class of solutions in odd dimensions to Einstein's equations
containing either a positive or negative cosmological constant. These solutions
resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added
feature of having Lorentzian signatures. They are asymptotic to
(A)dS. In the AdS case their energy is negative relative to that of
pure AdS. We present perturbative evidence in 5 dimensions that such metrics
are the states of lowest energy in their asymptotic class, and present a
conjecture that this is generally true for all such metrics. In the dS case
these solutions have a cosmological horizon. We show that their mass at future
infinity is less than that of pure dS.Comment: 26 pages, Late
The Hamiltonian Structure of the Second Painleve Hierarchy
In this paper we study the Hamiltonian structure of the second Painleve
hierarchy, an infinite sequence of nonlinear ordinary differential equations
containing PII as its simplest equation. The n-th element of the hierarchy is a
non linear ODE of order 2n in the independent variable depending on n
parameters denoted by and . We introduce new
canonical coordinates and obtain Hamiltonians for the and
evolutions. We give explicit formulae for these Hamiltonians showing that they
are polynomials in our canonical coordinates
Dynamics of a lattice Universe
We find a solution to Einstein field equations for a regular toroidal lattice
of size L with equal masses M at the centre of each cell; this solution is
exact at order M/L. Such a solution is convenient to study the dynamics of an
assembly of galaxy-like objects. We find that the solution is expanding (or
contracting) in exactly the same way as the solution of a
Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average
density as our model. This points towards the absence of backreaction in a
Universe filled with an infinite number of objects, and this validates the
fluid approximation, as far as dynamics is concerned, and at the level of
approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum
Gravit
Integrable discretizations of derivative nonlinear Schroedinger equations
We propose integrable discretizations of derivative nonlinear Schroedinger
(DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation
and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS
systems admit the reduction of complex conjugation between two dependent
variables and possess bi-Hamiltonian structure. Through transformations of
variables and reductions, we obtain novel integrable discretizations of the
nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS,
matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and
Burgers equations. We also discuss integrable discretizations of the
sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio
Scalar field and electromagnetic perturbations on Locally Rotationally Symmetric spacetimes
We study scalar field and electromagnetic perturbations on Locally
Rotationally Symmetric (LRS) class II spacetimes, exploiting a recently
developed covariant and gauge-invariant perturbation formalism. From the
Klein-Gordon equation and Maxwell's equations, respectively, we derive
covariant and gauge-invariant wave equations for the perturbation variables and
thereby find the generalised Regge-Wheeler equations for these LRS class II
spacetime perturbations. As illustrative examples, the results are discussed in
detail for the Schwarzschild and Vaidya spacetime, and briefly for some classes
of dust Universes.Comment: 22 pages; v3 has minor changes to match published versio
New variable separation approach: application to nonlinear diffusion equations
The concept of the derivative-dependent functional separable solution, as a
generalization to the functional separable solution, is proposed. As an
application, it is used to discuss the generalized nonlinear diffusion
equations based on the generalized conditional symmetry approach. As a
consequence, a complete list of canonical forms for such equations which admit
the derivative-dependent functional separable solutions is obtained and some
exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig
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