191 research outputs found
Quantized W-algebra of sl(2,1) and quantum parafermions of U_q(sl(2))
In this paper, we establish the connection between the quantized W-algebra of
and quantum parafermions of that a
shifted product of the two quantum parafermions of
generates the quantized W-algebra of
On Soliton-type Solutions of Equations Associated with N-component Systems
The algebraic geometric approach to -component systems of nonlinear
integrable PDE's is used to obtain and analyze explicit solutions of the
coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to
anti-kink transitions and multi-peaked soliton solutions is carried out.
Transformations are used to connect these solutions to several other equations
that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure
Peakons, R-Matrix and Toda-Lattice
The integrability of a family of hamiltonian systems, describing in a
particular case the motionof N ``peakons" (special solutions of the so-called
Camassa-Holm equation) is established in the framework of the -matrix
approach, starting from its Lax representation. In the general case, the
-matrix is a dynamical one and has an interesting though complicated
structure. However, for a particular choice of the relevant parameters in the
hamiltonian (the one corresponding to the pure ``peakons" case), the -matrix
becomes essentially constant, and reduces to the one pertaining to the finite
(non-periodic) Toda lattice. Intriguing consequences of such property are
discussed and an integrable time discretisation is derived.Comment: 12 plain tex page
A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions
An explicit reciprocal transformation between a 2-component generalization of
the Camassa-Holm equation, called the 2-CH system, and the first negative flow
of the AKNS hierarchy is established, this transformation enables one to obtain
solutions of the 2-CH system from those of the first negative flow of the AKNS
hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH
system are presented.Comment: 15 pages, 16 figures, some typos correcte
Tension and stiffness of the hard sphere crystal-fluid interface
A combination of fundamental measure density functional theory and Monte
Carlo computer simulation is used to determine the orientation-resolved
interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid
interface. Microscopic density functional theory is in quantitative agreement
with simulations and predicts a tension of 0.66 kT/\sigma^2 with a small
anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/\sigma^2 for the
(001) orientation and 1.03 kT/\sigma^2 for the (111) orientation. Here kT is
denoting the thermal energy and \sigma the hard sphere diameter. We compare our
results with existing experimental findings
65 лет издательской деятельности «Бюллетеня ОСЖД»
The OSJD Bulletin – the edition of the Organization for Co-Operation between Railways – celebrates its 65th anniversary. Being of the same age as the organisation itself, Bulletin has been diligently informing about its activities, acquainted the readers with all their aspects, and with the achievements of its members, revealed the most important projects, popularised scientific and engineering ideas. With the kind consent of our colleagues from editorial board of OSJD Bulletin, we present the main content of the article by the OSJD Committee Chairman Miroslaw Antonowicz and Editor-in-Chief Sergey Kabenkov published in the anniversary issue.В этом году Бюллетень ОСЖД – издание Организации сотрудничества железных дорог – отмечает 65-летний юбилей. Будучи практически ровесником самой организации, Бюллетень все эти годы неустанно освещал её деятельность, доносил до читателей информацию обо всех её сторонах, а также о достижениях её членов, рассказывал о важнейших проектах, популяризировал научно-технические идеи. Представляем с согласия наших коллег из редакции «Бюллетеня ОСЖД» основное содержание статьи Председателя Комитета ОСЖД М. Антоновича и главного редактора Бюллетеня ОСЖД С. Кабенкова из вышедшего по этому случаю юбилейного номера
Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions
We show how to generate coupled KdV hierarchies from Staeckel separable
systems of Benenti type. We further show that solutions of these Staeckel
systems generate a large class of finite-gap and rational solutions of cKdV
hierarchies. Most of these solutions are new.Comment: 15 page
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
Generalized r-matrix structure and algebro-geometric solution for integrable systems
The purpose of this paper is to construct a generalized r-matrix structure of
finite dimensional systems and an approach to obtain the algebro-geometric
solutions of integrable nonlinear evolution equations (NLEEs). Our starting
point is a generalized Lax matrix instead of usual Lax pair. The generalized
r-matrix structure and Hamiltonian functions are presented on the basis of
fundamental Poisson bracket. It can be clearly seen that various nonlinear
constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV,
c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure.
All these nonlinear systems have {\it r}-matrices, and are completely
integrable in Liouville's sense. Furthermore, our generalized structure is
developed to become an approach to obtain the algebro-geometric solutions of
integrable NLEEs. Finally, the two typical examples are considered to
illustrate this approach: the infinite or periodic Toda lattice equation and
the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure
Classical Poisson structures and r-matrices from constrained flows
We construct the classical Poisson structure and -matrix for some finite
dimensional integrable Hamiltonian systems obtained by constraining the flows
of soliton equations in a certain way. This approach allows one to produce new
kinds of classical, dynamical Yang-Baxter structures. To illustrate the method
we present the -matrices associated with the constrained flows of the
Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a
2-dimensional eigenvalue problem. Some of the obtained -matrices depend only
on the spectral parameters, but others depend also on the dynamical variables.
For consistency they have to obey a classical Yang-Baxter-type equation,
possibly with dynamical extra terms.Comment: 16 pages in LaTe
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