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Перегляд Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік за датою випуску

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Перегляд Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік за датою випуску

Сортувати за: Порядок: Результатів:

  • Spectral Analysis of Certain Schrödinger Operators 
    Ismail, Mourad E.H.; Koelink, E (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral ...
  • Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time 
    Garifullin, R.; Habibullin, I.; Yangubaeva, M. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras AN, BN, CN, G₂, D₃, A₁⁽¹⁾, A₂⁽²⁾, DN⁽²⁾ these systems are proved to be ...
  • Singular Isotonic Oscillator, Supersymmetry and Superintegrability 
    Marquette, I. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    In the case of a one-dimensional nonsingular Hamiltonian H and a singular supersymmetric partner Hα, the Darboux and factorization relations of supersymmetric quantum mechanics can be only formal relations. It was shown ...
  • Orbit Representations from Linear mod 1 Transformations 
    Correia Ramos, C.; Martins, N.; Pinto, P.R. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    We show that every point x0∈[0,1] carries a representation of a C∗-algebra that encodes the orbit structure of the linear mod 1 interval map fβ,α(x)=βx+α. Such C∗-algebra is generated by partial isometries arising from the ...
  • Complex SUSY Transformations and the Painlevé IV Equation 
    Bermúdez, D. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    In this paper we will explicitly work out the complex first-order SUSY transformation for the harmonic oscillator in order to obtain both real and complex new exactly-solvable potentials. Furthermore, we will show that ...
  • Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy 
    Musso, E. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. ...
  • Superintegrable Extensions of Superintegrable Systems 
    Chanu, C.M.; Degiovanni, L.; Rastelli, G. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    A procedure to extend a superintegrable system into a new superintegrable one is systematically tested for the known systems on E² and S² and for a family of systems defined on constant curvature manifolds. The procedure ...
  • Superintegrable Stäckel Systems on the Plane: Elliptic and Parabolic Coordinates 
    Tsiganov, A.V. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    Recently we proposed a generic construction of the additional integrals of motion for the Stäckel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle ...
  • On the Relations between Gravity and BF Theories 
    Freidel, L.; Speziale, S. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    We review, in the light of recent developments, the existing relations between gravity and topological BF theories at the classical level. We include the Plebanski action in both self-dual and non-chiral formulations, their ...
  • A Top-Down Account of Linear Canonical Transforms 
    Wolf, K.B. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    We contend that what are called Linear Canonical Transforms (LCTs) should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel representation found by ...
  • Old and New Reductions of Dispersionless Toda Hierarchy 
    Takasaki, K. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of ''Landau-Ginzburg potentials'' that play the ...
  • Note on Dilogarithm Identities from Nilpotent Double Affine Hecke Algebras 
    Nakanishi, T. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    Recently Cherednik and Feigin [arXiv:1209.1978] obtained several Rogers-Ramanujan type identities via the nilpotent double affine Hecke algebras (Nil-DAHA). These identities further led to a series of dilogarithm identities, ...
  • Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases 
    Maltsev, A.Y. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    In this paper we examine in detail the procedure of averaging of the local field-theoretic Poisson brackets proposed by B.A. Dubrovin and S.P. Novikov for the method of Whitham. The main attention is paid to the questions ...
  • Geometry of Spectral Curves and All Order Dispersive Integrable System 
    Borot, G.; Eynard, B. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    We propose a definition for a Tau function and a spinor kernel (closely related to Baker-Akhiezer functions), where times parametrize slow (of order 1/N) deformations of an algebraic plane curve. This definition consists ...
  • Note on Dilogarithm Identities from Nilpotent Double Affine Hecke Algebras 
    Nakanishi, T. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    Recently Cherednik and Feigin [arXiv:1209.1978] obtained several Rogers-Ramanujan type identities via the nilpotent double affine Hecke algebras (Nil-DAHA). These identities further led to a series of dilogarithm identities, ...
  • On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials 
    Roffelsen, P. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    We study the real roots of the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. It has been conjectured that the number of real roots of ...
  • Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations 
    Muriel, C.; Romero, J.L. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of λ-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the ...
  • Separation of Variables and Contractions on Two-Dimensional Hyperboloid 
    Kalnins, E.; Pogosyan, G.S.; Yakhno, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    In this paper analytic contractions have been established in the R→∞ contraction limit for exactly solvable basis functions of the Helmholtz equation on the two-dimensional two-sheeted hyperboloid. As a consequence we ...
  • Renormalization Method and Mirror Symmetry 
    Li, S. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    This is a brief summary of our works [arXiv:1112.4063, arXiv:1201.4501] on constructing higher genus B-model from perturbative quantization of BCOV theory. We analyze Givental's symplectic loop space formalism in the context ...
  • Solutions of Helmholtz and Schrödinger Equations with Side Condition and Nonregular Separation of Variables 
    Broadbridge, P.; Chanu, C.M.; Miller Jr., Willard (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
    Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional ...

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