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Volumn 46, Issue 3, 1998, Pages 189-205

Hamiltonian Structure of Non-Abelian Toda Lattice

Author keywords

Complete integrability; Lie Poisson brackets; Non Abelian Toda lattice; Rational matrix functions

Indexed keywords


EID: 0039071800     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007579806383     Document Type: Article
Times cited : (21)

References (22)
  • 1
    • 0001360991 scopus 로고
    • Isospectral Hamiltonian flows in finite and infinite dimensions II
    • Adams, M. R., Harnad, J. and Hurtubise, J.: Isospectral Hamiltonian flows in finite and infinite dimensions II, Comm. Math. Phys. 134 (1990), 555-585.
    • (1990) Comm. Math. Phys. , vol.134 , pp. 555-585
    • Adams, M.R.1    Harnad, J.2    Hurtubise, J.3
  • 2
    • 0013101025 scopus 로고
    • Darboux coordinates and Liouville-Arnold integration in loop algebras
    • Adams, M. R., Harnad, J. and Hurtubise, J.: Darboux coordinates and Liouville-Arnold integration in loop algebras, Comm. Math. Phys. 155 (1993), 385-413.
    • (1993) Comm. Math. Phys. , vol.155 , pp. 385-413
    • Adams, M.R.1    Harnad, J.2    Hurtubise, J.3
  • 3
    • 0003316646 scopus 로고
    • Expansions in Eigenfunctions of Selfadjoint Operators
    • Amer. Math. Soc., Providence
    • Berezansky, Yu. M.: Expansions in Eigenfunctions of Selfadjoint Operators, Trans. Math. Monogr. 17, Amer. Math. Soc., Providence, 1968.
    • (1968) Trans. Math. Monogr. 17
    • Berezansky, Yu.M.1
  • 4
    • 0002397530 scopus 로고
    • The integration of semi-infinite Toda chain by means of inverse spectral problem
    • Berezansky, Yu. M.: The integration of semi-infinite Toda chain by means of inverse spectral problem, Rep. Math. Phys. 24 (1986), 21-47.
    • (1986) Rep. Math. Phys. , vol.24 , pp. 21-47
    • Berezansky, Yu.M.1
  • 5
    • 0010011441 scopus 로고
    • Inverse problem of spectral analysis and non-Abelian chains of nonlinear equations
    • Berezansky, Yu. M. and Gekhtman, M.: Inverse problem of spectral analysis and non-Abelian chains of nonlinear equations, Ukrainian Math. J. 42 (1990), 645-658.
    • (1990) Ukrainian Math. J. , vol.42 , pp. 645-658
    • Berezansky, Yu.M.1    Gekhtman, M.2
  • 6
    • 34250104952 scopus 로고
    • Integration of certain chains of nonlinear difference equations by the method of the inverse spectral problem
    • Berezansky, Yu. M., Gekhtman, M. and Shmoish, M.: Integration of certain chains of nonlinear difference equations by the method of the inverse spectral problem, Ukrainian Math. J. 38 (1986), 84-89.
    • (1986) Ukrainian Math. J. , vol.38 , pp. 84-89
    • Berezansky, Yu.M.1    Gekhtman, M.2    Shmoish, M.3
  • 7
    • 0026104952 scopus 로고
    • Toda flows, inverse spectral transform and realization theory
    • Brockett, R. W. and Faybusovich, L. F.: Toda flows, inverse spectral transform and realization theory, Systems Control Lett. 16 (1991), 79-88.
    • (1991) Systems Control Lett. , vol.16 , pp. 79-88
    • Brockett, R.W.1    Faybusovich, L.F.2
  • 8
    • 36749105391 scopus 로고
    • The non-Abelian Toda lattice (discrete analogue of the matrix Schrödinger spectral problem)
    • Brushi, M., Manakov, S. V., Ragnisco, O. and Levi, D.: The non-Abelian Toda lattice (discrete analogue of the matrix Schrödinger spectral problem), J. Math. Phys. 21 (1980), 2749-2753.
    • (1980) J. Math. Phys. , vol.21 , pp. 2749-2753
    • Brushi, M.1    Manakov, S.V.2    Ragnisco, O.3    Levi, D.4
  • 10
    • 0031539416 scopus 로고    scopus 로고
    • Factorization of differential operators, quasideterminants, and non-Abelian Toda field equations
    • Etingof, P., Gelgand, I. M. and Retakh, V.: Factorization of differential operators, quasideterminants, and non-Abelian Toda field equations, Math. Res. Lett. 4 (1997), 413-425.
    • (1997) Math. Res. Lett. , vol.4 , pp. 413-425
    • Etingof, P.1    Gelgand, I.M.2    Retakh, V.3
  • 13
    • 1842721422 scopus 로고
    • Integration of non-Abelian chains of Toda type
    • Gekhtman, M.: Integration of non-Abelian chains of Toda type, Funct. Anal. Appl. 25 (1991), 230-232.
    • (1991) Funct. Anal. Appl. , vol.25 , pp. 230-232
    • Gekhtman, M.1
  • 14
    • 21344489864 scopus 로고
    • Non-Abelian nonlinear lattice equations of finite interval
    • Gekhtman, M.: Non-Abelian nonlinear lattice equations of finite interval, J. Phys. A 26 (1993), 6303-6317.
    • (1993) J. Phys. A , vol.26 , pp. 6303-6317
    • Gekhtman, M.1
  • 15
    • 21844486592 scopus 로고
    • Separation of variables in the classical SL(N) magnetic chain
    • Gekhtman, M.: Separation of variables in the classical SL(N) magnetic chain, Comm. Math. Phys. 167 (1995), 593-605.
    • (1995) Comm. Math. Phys. , vol.167 , pp. 593-605
    • Gekhtman, M.1
  • 16
    • 0000876641 scopus 로고
    • The solution to a generalized Toda lattice and representation theory
    • Kostant, B.: The solution to a generalized Toda lattice and representation theory, Adv. Math. 34 (1979), 195-338.
    • (1979) Adv. Math. , vol.34 , pp. 195-338
    • Kostant, B.1
  • 17
    • 0008026785 scopus 로고
    • The periodic non-Abelian Toda chain and its two-dimensional generalization
    • Krichever, I.: The periodic non-Abelian Toda chain and its two-dimensional generalization, Russian Math. Surveys 36 (1981), 82-89.
    • (1981) Russian Math. Surveys , vol.36 , pp. 82-89
    • Krichever, I.1
  • 18
    • 0000044682 scopus 로고
    • Integrable Hamiltonian systems connected with graded Lie algebras
    • Reyman, A. G.: Integrable Hamiltonian systems connected with graded Lie algebras, J. Soviet Math. 19 (1982), 1507-1545.
    • (1982) J. Soviet Math. , vol.19 , pp. 1507-1545
    • Reyman, A.G.1
  • 19
    • 0003270559 scopus 로고
    • Group-theoretical methods in the theory of finite-dimensional integrable systems
    • Encyclopedia of Math. Sci., Springer-Verlag, Berlin
    • Reyman, A. G. and Semenov-Tian-Shansky, M. A.: Group-theoretical methods in the theory of finite-dimensional integrable systems, Dynamical Systems VII, Encyclopedia of Math. Sci., Springer-Verlag, Berlin, 1994.
    • (1994) Dynamical Systems VII
    • Reyman, A.G.1    Semenov-Tian-Shansky, M.A.2
  • 20
    • 21844481908 scopus 로고
    • Classical functional Bethe Ansatz for SL(N): Separation of variables for the magnetic chain
    • Scott, D.R.D.: Classical functional Bethe Ansatz for SL(N): separation of variables for the magnetic chain, J. Math. Phys. 35 (1994), 5831-5843.
    • (1994) J. Math. Phys. , vol.35 , pp. 5831-5843
    • Scott, D.R.D.1
  • 21
    • 21344498585 scopus 로고
    • On generalized spectral functions, the parametrization of block Hankel and block Jacobi matrices, and some root location problems
    • Shmoish, M.: On generalized spectral functions, the parametrization of block Hankel and block Jacobi matrices, and some root location problems, Linear Algebra Appl. 202 (1994), 91-128.
    • (1994) Linear Algebra Appl. , vol.202 , pp. 91-128
    • Shmoish, M.1
  • 22
    • 34250248977 scopus 로고
    • Systems of Toda type, inverse spectral problems, and representation theory
    • Symes, W.: Systems of Toda type, inverse spectral problems, and representation theory, Invent. Math. 59 (1980), 13-51.
    • (1980) Invent. Math. , vol.59 , pp. 13-51
    • Symes, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.