709 research outputs found
Bulk correlation functions in 2D quantum gravity
We compute bulk 3- and 4-point tachyon correlators in the 2d Liouville
gravity with non-rational matter central charge c<1, following and comparing
two approaches. The continuous CFT approach exploits the action on the tachyons
of the ground ring generators deformed by Liouville and matter ``screening
charges''. A by-product general formula for the matter 3-point OPE structure
constants is derived. We also consider a ``diagonal'' CFT of 2D quantum
gravity, in which the degenerate fields are restricted to the diagonal of the
semi-infinite Kac table. The discrete formulation of the theory is a
generalization of the ADE string theories, in which the target space is the
semi-infinite chain of points.Comment: 14 pages, 2 figure
Bose-Einstein condensates with F=1 and F=2. Reductions and soliton interactions of multi-component NLS models
We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS)
related to the symmetric BD.I-type symmetric spaces and their reductions. We
briefly outline the direct and the inverse scattering method for the relevant
Lax operators and the soliton solutions. We use the Zakharov-Shabat dressing
method to obtain the two-soliton solution and analyze the soliton interactions
of the MNLS equations and some of their reductions.Comment: SPIE UNO-09-UN101-19, SPIE Volume: 7501, (2009
Fordy-Kulish models and spinor Bose-Einstein condensates
A three-component nonlinear Schrodinger-type model which describes spinor
Bose-Einstein condensate (BEC) is considered. This model is integrable by the
inverse scattering method and using Zakharov-Shabat dressing method we obtain
three types of soliton solutions. The multi-component nonlinear Schrodinger
type models related to symmetric spaces C.I Sp(4)/U(2) is studied.Comment: 8 pages, LaTeX, jnmp styl
New Integrable Multi-Component NLS Type Equations on Symmetric Spaces: Z_4 and Z_6 Reductions
The reductions of the multi-component nonlinear Schrodinger (MNLS) type
models related to C.I and D.III type symmetric spaces are studied. We pay
special attention to the MNLS related to the sp(4), so(10) and so(12) Lie
algebras. The MNLS related to sp(4) is a three-component MNLS which finds
applications to Bose-Einstein condensates. The MNLS related to so(12) and
so(10) Lie algebras after convenient Z_6 or Z_4 reductions reduce to three and
four-component MNLS showing new types of chi ^(3)-interactions that are
integrable. We briefly explain how these new types of MNLS can be integrated by
the inverse scattering method. The spectral properties of the Lax operators L
and the corresponding recursion operator Lambda are outlined. Applications to
spinor model of Bose-Einstein condensates are discussed.Comment: Reported to the Seventh International conference "Geometry,
Integrability and Quantization", June 2--10, 2005, Varna, Bulgari
Quasiperiodic Solutions of the Fibre Optics Coupled Nonlinear Schr{\"o}dinger Equations
We consider travelling periodical and quasiperiodical waves in single mode
fibres, with weak birefringence and under the action of cross-phase modulation.
The problem is reduced to the ``1:2:1" integrable case of the two-particle
quartic potential. A general approach for finding elliptic solutions is given.
New solutions which are associated with two-gap Treibich-Verdier potentials are
found. General quasiperiodic solutions are given in terms of two dimensional
theta functions with explicit expressions for frequencies in terms of theta
constants. The reduction of quasiperiodic solutions to elliptic functions is
discussed.Comment: 24 page
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