1,261 research outputs found
Some Remarks on the KP System of the Camassa-Holm Hierarchy
We study a Kadomtsev-Petviashvili system for the local Camassa-Holm hierarchy
obtaining a candidate to the Baker-Akhiezer function for its first reduction
generalizing the local Camassa-Holm. We focus our attention on the differences
with the standard KdV-KP case.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects
of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in
SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Hamiltonian motions of plane curves and formation of singularities and bubbles
A class of Hamiltonian deformations of plane curves is defined and studied.
Hamiltonian deformations of conics and cubics are considered as illustrative
examples. These deformations are described by systems of hydrodynamical type
equations. It is shown that solutions of these systems describe processes of
formation of singularities (cusps, nodes), bubbles, and change of genus of a
curve.Comment: 15 pages, 12 figure
Cohomological, Poisson structures and integrable hierarchies in tautological subbundles for Birkhoff strata of Sato Grassmannian
Cohomological and Poisson structures associated with the special tautological
subbundles for the Birkhoff strata of Sato Grassmannian
are considered. It is shown that the tangent bundles of
are isomorphic to the linear spaces of coboundaries with vanishing
Harrison's cohomology modules. Special class of 2-coboundaries is provided by
the systems of integrable quasilinear PDEs. For the big cell it is the dKP
hierarchy. It is demonstrated also that the families of ideals for algebraic
varieties in can be viewed as the Poisson ideals. This
observation establishes a connection between families of algebraic curves in
and coisotropic deformations of such curves of zero and
nonzero genus described by hierarchies of hydrodynamical type systems like dKP
hierarchy. Interrelation between cohomological and Poisson structures is noted.Comment: 15 pages, no figures, accepted in Theoretical and Mathematical
Physics. arXiv admin note: text overlap with arXiv:1005.205
Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems
Structure and properties of families of critical points for classes of
functions obeying the elliptic Euler-Poisson-Darboux equation
are studied. General variational and differential equations
governing the dependence of critical points in variational (deformation)
parameters are found. Explicit examples of the corresponding integrable
quasi-linear differential systems and hierarchies are presented There are the
extended dispersionless Toda/nonlinear Schr\"{o}dinger hierarchies, the
"inverse" hierarchy and equations associated with the real-analytic Eisenstein
series among them. Specific bi-Hamiltonian
structure of these equations is also discussed.Comment: 18 pages, no figure
Birkhoff strata of Sato Grassmannian and algebraic curves
Algebraic and geometric structures associated with Birkhoff strata of Sato
Grassmannian are analyzed. It is shown that each Birkhoff stratum
contains a subset of points for which each fiber of the
corresponding tautological subbundle is closed with respect to
multiplication. Algebraically is an infinite family of
infinite-dimensional commutative associative algebras and geometrically it is
an infinite tower of families of algebraic curves. For the big cell the
subbundle represents the tower of families of normal
rational (Veronese) curves of all degrees. For such tautological
subbundle is the family of coordinate rings for elliptic curves. For higher
strata, the subbundles represent families of plane
curves (trigonal curves at ) and space curves of genus .
Two methods of regularization of singular curves contained in
, namely, the standard blowing-up and transition to higher
strata with the change of genus are discussed.Comment: 31 pages, no figures, version accepted in Journal of Nonlinear
Mathematical Physics. The sections on the integrable systems present in
previous versions has been published separatel
Electron-phonon superconductivity in PtP compounds: from weak to strong coupling
We study the newly discovered Pt phosphides PtP (=Sr, Ca, La) [ T.
Takayama et al. Phys. Rev. Lett. 108, 237001 (2012)] using first-principles
calculations and Migdal-Eliashberg theory. Given the remarkable agreement with
the experiment, we exclude the charge-density wave scenario proposed by
previous first-principles calculations, and give conclusive answers concerning
the superconducting state in these materials. The pairing increases from La to
Ca and Sr due to changes in the electron-phonon matrix elements and
low-frequency phonons. Although we find that all three compounds are well
described by conventional s-wave superconductivity and spin-orbit coupling of
Pt plays a marginal role, we show that it could be possible to tune the
structure from centrosymmetric to noncentrosymmetric opening new perspectives
towards the understanding of unconventional superconductivity.Comment: updated Journal referenc
Plane waves from double extended spacetimes
We study exact string backgrounds (WZW models) generated by nonsemisimple
algebras which are obtained as double extensions of generic D--dimensional
semisimple algebras. We prove that a suitable change of coordinates always
exists which reduces these backgrounds to be the product of the nontrivial
background associated to the original algebra and two dimensional Minkowski.
However, under suitable contraction, the algebra reduces to a Nappi--Witten
algebra and the corresponding spacetime geometry, no more factorized, can be
interpreted as the Penrose limit of the original background. For both
configurations we construct D--brane solutions and prove that {\em all} the
branes survive the Penrose limit. Therefore, the limit procedure can be used to
extract informations about Nappi--Witten plane wave backgrounds in arbitrary
dimensions.Comment: 27 pages, no figures, references adde
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