87 research outputs found
Continuum limit of the Volterra model, separation of variables and non standard realizations of the Virasoro Poisson bracket
The classical Volterra model, equipped with the Faddeev-Takhtadjan Poisson
bracket provides a lattice version of the Virasoro algebra. The Volterra model
being integrable, we can express the dynamical variables in terms of the so
called separated variables. Taking the continuum limit of these formulae, we
obtain the Virasoro generators written as determinants of infinite matrices,
the elements of which are constructed with a set of points lying on an infinite
genus Riemann surface. The coordinates of these points are separated variables
for an infinite set of Poisson commuting quantities including . The
scaling limit of the eigenvector can also be calculated explicitly, so that the
associated Schroedinger equation is in fact exactly solvable.Comment: Latex, 43 pages Synchronized with the to be published versio
A method for obtaining Darboux transformations
In this paper we give a method to obtain Darboux transformations (DTs) of
integrable equations. As an example we give a DT of the dispersive water wave
equation. Using the Miura map, we also obtain the DT of the Jaulent-Miodek
equation. \end{abstract
Ferromagnetic properties of charged vector boson condensate
Bose-Einstein condensation of W bosons in the early universe is studied. It
is shown that, in the broken phase of the standard electroweak theory,
condensed W bosons form a ferromagnetic state with aligned spins. In this case
the primeval plasma may be spontaneously magnetized inside macroscopically
large domains and form magnetic fields which may be seeds for the observed
today galactic and intergalactic fields. However, in a modified theory, e.g. in
a theory without quartic self interactions of gauge bosons or for a smaller
value of the weak mixing angle, antiferromagnetic condensation is possible. In
the latter case W bosons form scalar condensate with macroscopically large
electric charge density i.e. with a large average value of the bilinear product
of W-vector fields but with microscopically small average value of the field
itself.Comment: Some numerical estimates and discussions are added according to the
referee's suggestions. This version is accepted for publication in JCA
Riemann-Hilbert problem for Hurwitz Frobenius manifolds: regular singularities
In this paper we study the Fuchsian Riemann-Hilbert (inverse monodromy)
problem corresponding to Frobenius structures on Hurwitz spaces. We find a
solution to this Riemann-Hilbert problem in terms of integrals of certain
meromorphic differentials over a basis of an appropriate relative homology
space, study the corresponding monodromy group and compute the monodromy
matrices explicitly for various special cases.Comment: final versio
Darboux Transformations for a Lax Integrable System in -Dimensions
A -dimensional Lax integrable system is proposed by a set of specific
spectral problems. It contains Takasaki equations, the self-dual Yang-Mills
equations and its integrable hierarchy as examples. An explicit formulation of
Darboux transformations is established for this Lax integrable system. The
Vandermonde and generalized Cauchy determinant formulas lead to a description
for deriving explicit solutions and thus some rational and analytic solutions
are obtained.Comment: Latex, 14 pages, to be published in Lett. Math. Phy
On Darboux-Treibich-Verdier potentials
It is shown that the four-parameter family of elliptic functions
introduced
by Darboux and rediscovered a hundred years later by Treibich and Verdier, is
the most general meromorphic family containing infinitely many finite-gap
potentials.Comment: 8 page
From nonassociativity to solutions of the KP hierarchy
A recently observed relation between 'weakly nonassociative' algebras A (for
which the associator (A,A^2,A) vanishes) and the KP hierarchy (with dependent
variable in the middle nucleus A' of A) is recalled. For any such algebra there
is a nonassociative hierarchy of ODEs, the solutions of which determine
solutions of the KP hierarchy. In a special case, and with A' a matrix algebra,
this becomes a matrix Riccati hierarchy which is easily solved. The matrix
solution then leads to solutions of the scalar KP hierarchy. We discuss some
classes of solutions obtained in this way.Comment: 7 pages, 4 figures, International Colloquium 'Integrable Systems and
Quantum Symmetries', Prague, 15-17 June 200
How to superize Liouville equation
So far, there are described in the literature two ways to superize the
Liouville equation: for a scalar field (for ) and for a vector-valued
field (analogs of the Leznov--Saveliev equations) for N=1. Both superizations
are performed with the help of Neveu--Schwarz superalgebra. We consider another
version of these superLiouville equations based on the Ramond superalgebra,
their explicit solutions are given by Ivanov--Krivonos' scheme. Open problems
are offered
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