NONLOCAL MATRIX HAMILTONIAN OPERATORS, DIFFERENTIAL GEOMETRY, AND APPLICATIONS

被引：14
|
作者：
FERAPONTOV, EV
机构：
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 1992年 / 91卷 / 03期
关键词：
D O I：
10.1007/BF01017341
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
A study is made of a class of nonlocal Hamiltonian operators that arise naturally as second Hamiltonian structures of the nonlinear Schrodinger equation, the Heisenberg magnet, the Landau-Lifshitz equation, etc. A complete description of these operators is obtained, and it reveals intimate connections with classical differential geometry. A new nonlocal Hamiltonian structure of first order is constructed for the partly anisotropic (J1 = J2) Landau-Lifshitz equation (hitherto, only Hamiltonian structures of zeroth and second orders were known for the Landau-Lifshitz equation).
引用
收藏
页码：642 / 649
页数：8
相关论文
共 50 条
  • [31] Geometry of differential operators on Weyl manifolds
    Bokan, N
    Gilkey, PB
    Simon, U
    PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1997, 453 (1967): : 2527 - 2536
  • [32] Symplectic geometry and dissipative differential operators
    Yao, Siqin
    Sun, Jiong
    Zettl, Anton
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 414 (01) : 434 - 449
  • [33] Differential Geometry for Nuclear Positive Operators
    Cristian Conde
    Integral Equations and Operator Theory, 2007, 57 : 451 - 471
  • [34] Differential geometry for nuclear positive operators
    Conde, Cristian
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 2007, 57 (04) : 451 - 471
  • [35] High order forces and nonlocal operators in a Kohn-Sham Hamiltonian
    Bobbitt, N. Scott
    Schofield, Grady
    Lena, Charles
    Chelikowsky, James R.
    PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 2015, 17 (47) : 31542 - 31549
  • [36] NONLOCAL HAMILTONIAN OPERATORS OF HYDRODYNAMIC TYPE RELATED TO METRICS OF CONSTANT CURVATURE
    MOKHOV, OI
    FERAPONTOV, EV
    RUSSIAN MATHEMATICAL SURVEYS, 1990, 45 (03) : 218 - 219
  • [37] DIFFERENTIAL GEOMETRY OF MATRIX INVERSION
    Huhtanen, Marko
    MATHEMATICA SCANDINAVICA, 2010, 107 (02) : 267 - 284
  • [38] Applications of Hofer's geometry to Hamiltonian dynamics
    Schlenk, F
    COMMENTARII MATHEMATICI HELVETICI, 2006, 81 (01) : 105 - 121
  • [39] Projective geometry of homogeneous second-order Hamiltonian operators
    Vergallo, Pierandrea
    Vitolo, Raffaele
    NONLINEARITY, 2023, 36 (10) : 5311 - 5333
  • [40] Nonlocal Fractional Differential Equations and Applications
    Veli Shakhmurov
    Complex Analysis and Operator Theory, 2020, 14
12345