137 research outputs found
Darboux transformation for classical acoustic spectral problem
We study discrete isospectral symmetries for the classical acoustic spectral
problem in spatial dimensions one and two, by developing a Darboux (Moutard)
transformation formalism for this problem. The procedure follows the steps,
similar to those for the Schr\"{o}dinger operator. However, there is no
one-to-one correspondence between the two problems. The technique developed
enables one to construct new families of integrable potentials for the acoustic
problem, in addition to those already known.
The acoustic problem produces a non-linear Harry Dym PDE. Using the
technique, we reproduce a pair of simple soliton solutions of this equation.
These solutions are further used to construct a new positon solution for this
PDE. Furthermore, using the dressing chain approach, we build a modified Harry
Dym equation together with its LA-pair.
As an application, we construct some singular and non-singular integrable
potentials (dielectric permitivity) for the Maxwell equations in a 2D
inhomogeneous medium.Comment: 16 pages; keywords Darboux (Moutard) transformation, Classical
acoustic spectral problem, Reflexionless potentials, Soliton
Comparison of the hydrodynamic and Dirac models of the dispersion interaction between graphene and H, He, or Na atoms
The van der Waals and Casimir-Polder interaction of different atoms with
graphene is investigated using the Dirac model which assumes that the energy of
quasiparticles is linear with respect to the momentum. The obtained results for
the van der Waals coefficients of hydrogen atoms and molecules and atoms of
metastable He and Na as a function of separation are compared with
respective results found using the hydrodynamic model of graphene. It is shown
that, regardless of the value of the gap parameter, the Dirac model leads to
much smaller values of the van der Waals coefficients than the hydrodynamic
model. The experiment on quantum reflection of metastable He and Na
atoms on graphene is proposed which is capable to discriminate between the two
models of the electronic structure of graphene. In this respect the parameters
of the phenomenological potential for both these atoms interacting with
graphene described by different models are determined.Comment: 15 pages, 4 figure
Two-component Analogue of Two-dimensional Long Wave-Short Wave Resonance Interaction Equations: A Derivation and Solutions
The two-component analogue of two-dimensional long wave-short wave resonance
interaction equations is derived in a physical setting. Wronskian solutions of
the integrable two-component analogue of two-dimensional long wave-short wave
resonance interaction equations are presented.Comment: 16 pages, 9 figures, revised version; The pdf file including all
figures: http://www.math.utpa.edu/kmaruno/yajima.pd
The Inverse Scattering Method, Lie-Backlund Transformations and Solitons for Low-energy Effective Field Equations of 5D String Theory
In the framework of the 5D low-energy effective field theory of the heterotic
string with no vector fields excited, we combine two non-linear methods in
order to construct a solitonic field configuration. We first apply the inverse
scattering method on a trivial vacuum solution and obtain an stationary
axisymmetric two-soliton configuration consisting of a massless gravitational
field coupled to a non-trivial chargeless dilaton and to an axion field endowed
with charge. The implementation of this method was done following a scheme
previously proposed by Yurova. We also show that within this scheme, is not
possible to get massive gravitational solitons at all. We then apply a
non-linear Lie-Backlund matrix transformation of Ehlers type on this massless
solution and get a massive rotating axisymmetric gravitational soliton coupled
to axion and dilaton fields endowed with charges. We study as well some
physical properties of the constructed massless and massive solitons and
discuss on the effect of the generalized solution generating technique on the
seed solution and its further generalizations.Comment: 17 pages in latex, changed title, improved text, added reference
Chiral models in dilaton-Maxwell gravity
We study symmetry properties of the Einstein-Maxwell theory nonminimaly
coupled to the dilaton field. We consider a static case with pure electric
(magnetic) Maxwell field and show that the resulting system becomes a nonlinear
sigma-model wich possesses a chiral representation. We construct the
corresponding chiral matrix and establish a representation which is related to
the pair of Ernst-like potentials. These potentials are used for separation of
the symmetry group into the gauge and nongauge (charging) sectors. New
variables, which linearize the action of charging symmetries, are also
established; a solution generation technique based on the use of charging
symmetries is formulated. This technique is used for generation of the
elecricaly (magneticaly) charged dilatonic fields from the static General
Relativity ones.Comment: 9 pages in LaTex; published in Gen. Rel. Grav. 32 (2000) pp 1389-139
U(1,1)--Invariant Generation of Charges for Einstein--Maxwell--Dilaton--Axion Theory
The action of the isometry subgroup which preserves the trivial values of the
fields is studied for the stationary D=4 Einstein--Maxwell--Dilaton--Axion
theory. The technique for generation of charges and the corresponding procedure
for construction of new solutions is formulated. A solution describing the
double rotating dyon with independent values of all physical charges is
presented.Comment: 14 pages, RevTex, no figurie
Soliton solution in dilaton-Maxwell gravity
The inverse scattering problem method application to construction of exact
solution for Maxwell dilaton gravity system ia considered. By use of Belinsky
and Zakharov L - A pair the solution of the theory is constructed. The rotating
Kerr - like configuration with NUT - parameter is obtained.Comment: 8 pages in LaTex; published in Gen. Rel. Grav. pp. 32 (2000)
2219-222
Ergodicity criteria for non-expanding transformations of 2-adic spheres
In the paper, we obtain necessary and sufficient conditions for ergodicity
(with respect to the normalized Haar measure) of discrete dynamical systems
on 2-adic spheres of radius
, , centered at some point from the ultrametric space of
2-adic integers . The map is
assumed to be non-expanding and measure-preserving; that is, satisfies a
Lipschitz condition with a constant 1 with respect to the 2-adic metric, and
preserves a natural probability measure on , the Haar measure
on which is normalized so that
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