18 research outputs found
The Lax Pair by Dimensional Reduction of Chern-Simons Gauge Theory
We show that the Nonlinear Schr\"odinger Equation and the related Lax pair in
1+1 dimensions can be derived from 2+1 dimensional Chern-Simons Topological
Gauge Theory. The spectral parameter, a main object for the Loop algebra
structure and the Inverse Spectral Transform, has appear as a homogeneous part
(condensate) of the statistical gauge field, connected with the compactified
extra space coordinate. In terms of solitons, a natural interpretation for the
one-dimensional analog of Chern-Simons Gauss law is given.Comment: 27 pages, Plain Te
Chern-Simons Field Theory and Completely Integrable Systems
We show that the classical non-abelian pure Chern-Simons action is related in
a natural way to completely integrable systems of the Davey-Stewartson
hyerarchy, via reductions of the gauge connection in Hermitian spaces and by
performing certain gauge choices. The B\"acklund Transformations are
interpreted in terms of Chern-Simons equations of motion or, on the other hand,
as a consistency condition on the gauge. A mapping with a nonlinear
-model is discussed.Comment: 11 pages, Late
Self-dual SU(2) invariant Einstein metrics and modular dependence of theta-functions
We simplify Hitchin's description of SU(2)-invariant self-dual Einstein
metrics, making use of the tau-function of related four-pole Schlesinger
system.Comment: A wrong sign in the formula for W_1 is corrected; we thank Owen
Dearricott who pointed out this mistake in the original version of the pape
Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrodinger operator
With this paper we begin an investigation of difference schemes that possess
Darboux transformations and can be regarded as natural discretizations of
elliptic partial differential equations. We construct, in particular, the
Darboux transformations for the general self adjoint schemes with five and
seven neighbouring points. We also introduce a distinguished discretization of
the two-dimensional stationary Schrodinger equation, described by a 5-point
difference scheme involving two potentials, which admits a Darboux
transformation.Comment: 15 pages, 1 figur
Unified approach to transformations of Painleve equations
Ankara : Department of Mathematics and Institute of Engineering and Sciences, Bilkent Univ., 1993.Thesis (Master's) -- Bilkent University, 1993.Includes bibliographical references leaves 36-37In this thesis, we iind the explicit form of some transformations associated
with the second, third, fourth and fifth Painleve equations. These
transformations are obtained by using the Schlesinger transformations
associated with the linear system of equations of Painleve eciuations.The
application of such transformations enables us to generate the new solutions
of the given Painleve equation with different values of parameters,
from the known solutions.Chahardehi, Ali Reza ModaressiM.S