259 research outputs found
On Darboux transformation of the supersymmetric sine-Gordon equation
Darboux transformation is constructed for superfields of the super
sine-Gordon equation and the superfields of the associated linear problem. The
Darboux transformation is shown to be related to the super B\"{a}cklund
transformation and is further used to obtain super soliton solutions.Comment: 9 Page
Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach
Here we have studied first and second-order intertwining approach to generate
isospectral partner potentials of position-dependent (effective) mass
Schroedinger equation. The second-order intertwiner is constructed directly by
taking it as second order linear differential operator with position depndent
coefficients and the system of equations arising from the intertwining
relationship is solved for the coefficients by taking an ansatz. A complete
scheme for obtaining general solution is obtained which is valid for any
arbitrary potential and mass function. The proposed technique allows us to
generate isospectral potentials with the following spectral modifications: (i)
to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the
spectrum unaffected. To explain our findings with the help of an illustration,
we have used point canonical transformation (PCT) to obtain the general
solution of the position dependent mass Schrodinger equation corresponding to a
potential and mass function. It is shown that our results are consistent with
the formulation of type A N-fold supersymmetry [14,18] for the particular case
N = 1 and N = 2 respectively.Comment: Some references have been adde
Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians,
we analyze three sets of complex potentials with real spectra, recently derived
by a potential algebraic approach based upon the complex Lie algebra sl(2, C).
This extends to the complex domain the well-known relationship between SUSYQM
and potential algebras for Hermitian Hamiltonians, resulting from their common
link with the factorization method and Darboux transformations. In the same
framework, we also generate for the first time a pair of elliptic partner
potentials of Weierstrass type, one of them being real and the other
imaginary and PT symmetric. The latter turns out to be quasiexactly solvable
with one known eigenvalue corresponding to a bound state. When the Weierstrass
function degenerates to a hyperbolic one, the imaginary potential becomes PT
non-symmetric and its known eigenvalue corresponds to an unbound state.Comment: 20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int.
J. Mod. Phys.
Complete list of Darboux Integrable Chains of the form
We study differential-difference equation of the form with unknown
depending on continuous and discrete variables and . Equation
of such kind is called Darboux integrable, if there exist two functions and
of a finite number of arguments , ,
, such that and , where
is the operator of total differentiation with respect to , and is
the shift operator: . Reformulation of Darboux integrability in
terms of finiteness of two characteristic Lie algebras gives an effective tool
for classification of integrable equations. The complete list of Darboux
integrable equations is given in the case when the function is of the
special form
Darboux transformations for a 6-point scheme
We introduce (binary) Darboux transformation for general differential
equation of the second order in two independent variables. We present a
discrete version of the transformation for a 6-point difference scheme. The
scheme is appropriate to solving a hyperbolic type initial-boundary value
problem. We discuss several reductions and specifications of the
transformations as well as construction of other Darboux covariant schemes by
means of existing ones. In particular we introduce a 10-point scheme which can
be regarded as the discretization of self-adjoint hyperbolic equation
Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models
New exactly solvable quantum models are obtained with the help of the
supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in
Physics". Dubna, Russia, 28 July - 2 August, 199
G´en´etique Clinique dans le Service de P´ediatrie et de G´en´etique M´edicale du Centre National Hospitalier et Universitaire de Cotonou : Etat des Lieux et Perspectives
Il s’agissait d’une ´etude r´etrospective descriptive portant sur les patients rec¸us en consultation de g´en´etique m´edicale de Septembre 2004 `a Aoˆut 2007. Les patients b´en´eficiaient des examens dysmorphologique et physique, des bilans cytog´en´etiques et/ou mol´eculaires, des interventions th´erapeutiques et un suivi `a long terme. Les variables ´etudi´ees ´etaient les donn´ees sociod´emographiques et cliniques. Soixante et seize patients ont ´et´e rec¸us durant la p´eriode avec une pr´edominance masculine (57,89%). Les motifs de consultation ´etaient domin´es par le retard psychomoteur (38,15%), la dysmorphie faciale (30,26%) et les malformations (19,73%). Les principales malformations portaient sur les extr´emit´es et la face. Les pathologies confirm´ees comprenaient des aberrations chromosomiques (46,05%) avec une pr´edominance de la trisomie 21 et des maladies monog´eniques (7,89%). Le rendement de nos recherches pourrait ˆetre am´elior´e par l’acc`es `a la technique FISH. C’est une exp´erience quasi unique en Afrique de l’ouest et permet d’apporter des r´eponses aux personnes souffrant d’affections h´er´editaires.Mots Cl´es g´en´etique clinique ; retard psychomoteur ; dysmorphie ; malformation ; aberration chromosomique ; maladie monog´eniqu
Integrability and explicit solutions in some Bianchi cosmological dynamical systems
The Einstein field equations for several cosmological models reduce to
polynomial systems of ordinary differential equations. In this paper we shall
concentrate our attention to the spatially homogeneous diagonal G_2
cosmologies. By using Darboux's theory in order to study ordinary differential
equations in the complex projective plane CP^2 we solve the Bianchi V models
totally. Moreover, we carry out a study of Bianchi VI models and first
integrals are given in particular cases
Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians
The Sukumar theorem about the connection between the Green functions of the
supersymmetric pair of the Schr\"odinger Hamiltonians is generalized to the
case of the supersymmetric pair of the Dirac Hamiltonians.Comment: 12 pages,Latex, no figure
Asymptotics of skew orthogonal polynomials
Exact integral expressions of the skew orthogonal polynomials involved in
Orthogonal (beta=1) and Symplectic (beta=4) random matrix ensembles are
obtained: the (even rank) skew orthogonal polynomials are average
characteristic polynomials of random matrices. From there, asymptotics of the
skew orthogonal polynomials are derived.Comment: 17 pages, Late
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