496 research outputs found
Toda lattice realization of integrable hierarchies
We present a new realization of scalar integrable hierarchies in terms of the
Toda lattice hierarchy. In other words, we show on a large number of examples
that an integrable hierarchy, defined by a pseudodifferential Lax operator, can
be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda
lattice hierarchy seems to be as general as the Drinfeld--Sokolov realization.Comment: 11 pages, Latex (minor changes, to appear in Lett.Math.Phys.
A remark on the asymptotic form of BPS multi-dyon solutions and their conserved charges
We evaluate the gauge invariant, dynamically conserved charges, recently
obtained from the integral form of the Yang-Mills equations, for the BPS
multi-dyon solutions of a Yang-Mills-Higgs theory associated to any compact
semi-simple gauge group G. Those charges are shown to correspond to the
eigenvalues of the next-to-leading term of the asymptotic form of the Higgs
field at spatial infinity, and so coinciding with the usual topological charges
of those solutions. Such results show that many of the topological charges
considered in the literature are in fact dynamical charges, which conservation
follows from the global properties of classical Yang-Mills theories encoded
into their integral dynamical equations. The conservation of those charges can
not be obtained from the differential form of Yang-Mills equations.Comment: Version to be published in JHEP, Journal of High Energy Physics (19
pages, no figures, some examples added
Regularity and stability of electrostatic solutions in Kaluza-Klein theory
We investigate the family of electrostatic spherically symmetric solutions of
the five-dimensional Kaluza-Klein theory. Besides black holes and wormholes, a
new class of geodesically complete solutions is identified. A monopole
perturbation is carried out, enabling us to prove analytically the stability of
a large class of solutions, including all black holes and neutral solutions.Comment: 2 pages, "mprocl.sty" with LATEX 2.09, contribution to the 9th Marcel
Grossmann meeting (MG9), Rome, July 200
Electrostatic solutions in Kaluza-Klein theory: geometry and stability
We investigate the family of electrostatic spherically symmetric solutions of
the five-dimensional Kaluza-Klein theory. Both charged and neutral cases are
considered. The analysis of the solutions, through their geometrical
properties, reveals the existence of black holes, wormholes and naked
singularities. A new class of regular solutions is identified. A monopole
perturbation study of all these solutions is carried out, enabling us to prove
analytically the stability of large classes of solutions. In particular, the
black hole solutions are stable, while for the regular solutions the stability
analysis leads to an eigenvalue problem.Comment: Latex file, 21 page
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