메뉴 건너뛰기




Volumn 7, Issue 2, 2000, Pages 213-243

Degenerate Poisson Pencils on Curves: New Separability Theory

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0347645808     PISSN: 14029251     EISSN: 17760852     Source Type: Journal    
DOI: 10.2991/jnmp.2000.7.2.7     Document Type: Article
Times cited : (19)

References (44)
  • 1
    • 0002681157 scopus 로고
    • Separation of Variables. New Trends
    • Sklyanin, E.K., 1995. Separation of Variables. New Trends. Prog. Theor. Phys. Suppl., 118:35
    • (1995) Prog. Theor. Phys. Suppl. , vol.118 , pp. 35
    • Sklyanin, E.K.1
  • 5
    • 0001033506 scopus 로고
    • Separable Systems of Stäckel
    • Eisenhart, L.P., 1934. Separable Systems of Stäckel. Ann. Math., 35:284
    • (1934) Ann. Math. , vol.35 , pp. 284
    • Eisenhart, L.P.1
  • 8
    • 0142053652 scopus 로고
    • Separation of Variables in the Gaudin Model
    • Sklyanin, E.K., 1989. Separation of Variables in the Gaudin Model. J. Sov. Math., 47:2473
    • (1989) J. Sov. Math. , vol.47 , pp. 2473
    • Sklyanin, E.K.1
  • 9
    • 21144467777 scopus 로고
    • Separation of Variables in the Classical Integrable SL(3) Magnetic Chain
    • Sklyanin, E.K., 1992. Separation of Variables in the Classical Integrable SL(3) Magnetic Chain. Commun. Math. Phys., 150:181
    • (1992) Commun. Math. Phys. , vol.150 , pp. 181
    • Sklyanin, E.K.1
  • 10
    • 0010739497 scopus 로고
    • Linear r-Matrix Algebra for Systems Separable in Parabolic Coordinates
    • Eilbeck, J.C., Enolskii, V.Z., Kuznetsov, V.B., and Legkin, D.V., 1993. Linear r-Matrix Algebra for Systems Separable in Parabolic Coordinates. Phys. Lett. A, 180:208
    • (1993) Phys. Lett. A , vol.180 , pp. 208
    • Eilbeck, J.C.1    Enolskii, V.Z.2    Kuznetsov, V.B.3    Legkin, D.V.4
  • 13
    • 0001521197 scopus 로고
    • Integrable Stationary Flows: Miura Maps and Bi-Hamiltonian Structures
    • Antonowicz, M., Fordy, A., and Wojciechowski, S., 1987. Integrable Stationary Flows:Miura Maps and Bi-Hamiltonian Structures. Phys. Lett. A, 124:143
    • (1987) Phys. Lett. A , vol.124 , pp. 143
    • Antonowicz, M.1    Fordy, A.2    Wojciechowski, S.3
  • 14
    • 45149136807 scopus 로고
    • Constrained Flows of Integrable PDE’s and Bi-Hamiltonian Structure of Garnier System
    • Antonowicz, M., and Rauch-Wojciechowski, S., 1990. Constrained Flows of Integrable PDE’s and Bi-Hamiltonian Structure of Garnier System. Phys. Lett. A, 147:455
    • (1990) Phys. Lett. A , vol.147 , pp. 455
    • Antonowicz, M.1    Rauch-Wojciechowski, S.2
  • 15
    • 36149034811 scopus 로고
    • Restricted Flows of Soliton Hierarchies: Coupled KdV and Harry Dym Case
    • Antonowicz, M., and Rauch-Wojciechowski, S., 1991. Restricted Flows of Soliton Hierarchies:Coupled KdV and Harry Dym Case. J. Phys. A:Gen. Math., 24:5043
    • (1991) J. Phys. A: Gen. Math. , vol.24 , pp. 5043
    • Antonowicz, M.1    Rauch-Wojciechowski, S.2
  • 16
    • 0001670729 scopus 로고
    • Bi-Hamiltonian Formulation of the Henon-Heiles Sys-tem and its Multi-Dimensional Extension
    • Antonowicz, M., and Rauch-Wojciechowski, S., 1992. Bi-Hamiltonian Formulation of the Henon-Heiles Sys-tem and its Multi-Dimensional Extension. Phys. Lett. A, 163:167
    • (1992) Phys. Lett. A , vol.163 , pp. 167
    • Antonowicz, M.1    Rauch-Wojciechowski, S.2
  • 17
    • 0000170469 scopus 로고
    • How to Constract Finite-Dimensional Bi-Hamiltonian Systems from Soliton Equations: Jacobi Integrable Potentials
    • Antonowicz, M., and Rauch-Wojciechowski, S., 1992. How to Constract Finite-Dimensional Bi-Hamiltonian Systems from Soliton Equations:Jacobi Integrable Potentials. J. Math. Phys. A:Gen. Math., 33:2115
    • (1992) J. Math. Phys. A: Gen. Math. , vol.33 , pp. 2115
    • Antonowicz, M.1    Rauch-Wojciechowski, S.2
  • 18
    • 0040390477 scopus 로고
    • Bi-Hamiltonian Dynamical Systems Related to Low-Dimensional Lie Algebras
    • Błaszak, M., and Wojciechowski, S., 1989. Bi-Hamiltonian Dynamical Systems Related to Low-Dimensional Lie Algebras. Physica A, 155:545
    • (1989) Physica A , vol.155 , pp. 545
    • Błaszak, M.1    Wojciechowski, S.2
  • 19
    • 0005233699 scopus 로고
    • Bi-Hamiltonian Formulation of a Finite Dimensional Integrable Systems Reduced from a Lax Hierarchy of the KdV
    • Błaszak, M., and Basarab-Horwath, P., 1992. Bi-Hamiltonian Formulation of a Finite Dimensional Integrable Systems Reduced from a Lax Hierarchy of the KdV. Phys. Lett. A, 171:45
    • (1992) Phys. Lett. A , vol.171 , pp. 45
    • Błaszak, M.1    Basarab-Horwath, P.2
  • 20
    • 0040390479 scopus 로고
    • Newton Representation of Nonlinear Ordinary Differential Equations
    • Błaszak, M., and Rauch-Wojciechowski, S., 1993. Newton Representation of Nonlinear Ordinary Differential Equations. Physica A, 197:191
    • (1993) Physica A , vol.197 , pp. 191
    • Błaszak, M.1    Rauch-Wojciechowski, S.2
  • 21
    • 21344484877 scopus 로고    scopus 로고
    • Miura Map and Bi-Hamiltonian Formulation for Restricted Flows of the KdV Hierarchy
    • Błaszak, M., Miura Map and Bi-Hamiltonian Formulation for Restricted Flows of the KdV Hierarchy. J. Phys. A:Gen. Math., 265985
    • J. Phys. A: Gen. Math. , vol.26 , pp. 5985
    • Błaszak, M.1
  • 22
    • 21344480811 scopus 로고
    • A Generalized Henon-Heiles System and Related Integrable Newton Equations
    • Błaszak, M., and Rauch-Wojciechowski, S., 1994. A Generalized Henon-Heiles System and Related Integrable Newton Equations. J. Math. Phys., 35:1693
    • (1994) J. Math. Phys. , vol.35 , pp. 1693
    • Błaszak, M.1    Rauch-Wojciechowski, S.2
  • 23
    • 0040984697 scopus 로고
    • Newton Representation for Stationary Flows of Some Class of Nonlinear Dynamical Systems
    • Błaszak, M., 1995. Newton Representation for Stationary Flows of Some Class of Nonlinear Dynamical Systems. Physica A, 215:201
    • (1995) Physica A , vol.215 , pp. 201
    • Błaszak, M.1
  • 24
    • 0030284185 scopus 로고    scopus 로고
    • Two Newton Decompositions of Stationary Flows of KdV and Harry Dym Hierarchies
    • Rauch-Wojciechowski, S., Marciniak, K., and Błaszak, M., 1996. Two Newton Decompositions of Stationary Flows of KdV and Harry Dym Hierarchies. Physica A, 233:307
    • (1996) Physica A , vol.233 , pp. 307
    • Rauch-Wojciechowski, S.1    Marciniak, K.2    Błaszak, M.3
  • 25
    • 0000079718 scopus 로고
    • A Bi-Hamiltonian Formulation for Separable Potentials and its Application to the Kepler Problem and the Euler Problem of Two Centers of Gravitation
    • Rauch-Wojciechowski, S., 1991. A Bi-Hamiltonian Formulation for Separable Potentials and its Application to the Kepler Problem and the Euler Problem of Two Centers of Gravitation. Phys. Lett. A, 160:149
    • (1991) Phys. Lett. A , vol.160 , pp. 149
    • Rauch-Wojciechowski, S.1
  • 26
    • 0032362858 scopus 로고    scopus 로고
    • On Separability of Bi-Hamiltonian Chain with Degenerated Poisson Structures
    • Błaszak, M., 1998. On Separability of Bi-Hamiltonian Chain with Degenerated Poisson Structures. J. Math. Phys., 39:3213
    • (1998) J. Math. Phys. , vol.39 , pp. 3213
    • Błaszak, M.1
  • 27
    • 0002031581 scopus 로고    scopus 로고
    • Bi-Hamiltonian Separable Chains on Riemannian Manifolds
    • Błaszak, M., 1998. Bi-Hamiltonian Separable Chains on Riemannian Manifolds. Phys. Lett. A, 243:25
    • (1998) Phys. Lett. A , vol.243 , pp. 25
    • Błaszak, M.1
  • 28
    • 0003406480 scopus 로고    scopus 로고
    • Multi-Hamiltonian Theory of Dynamical Systems
    • Springer-Verlag
    • Błaszak, M., 1998. “Multi-Hamiltonian Theory of Dynamical Systems”. In Texts and Monographs in Physics, Springer-Verlag.
    • (1998) Texts and Monographs in Physics
    • Błaszak, M.1
  • 29
    • 0034348916 scopus 로고    scopus 로고
    • Inverse Bi-Hamiltonian Separable Chains
    • press
    • Błaszak, M., 2000. Inverse Bi-Hamiltonian Separable Chains. J. Theor. Math. Phys., in press
    • (2000) J. Theor. Math. Phys.
    • Błaszak, M.1
  • 30
    • 0033240089 scopus 로고    scopus 로고
    • Theory of Separability of Multi-Hamiltonian Chains
    • Błaszak, M., 1999. Theory of Separability of Multi-Hamiltonian Chains. J. Math. Phys., 40:5725
    • (1999) J. Math. Phys. , vol.40 , pp. 5725
    • Błaszak, M.1
  • 31
    • 0034238534 scopus 로고    scopus 로고
    • Separability of Two-Casimir Bi- and Tri-Hamiltonian Chains
    • press
    • Błaszak, M., 2000. Separability of Two-Casimir Bi- and Tri-Hamiltonian Chains. Rep. Math. Phys., in press
    • (2000) Rep. Math. Phys.
    • Błaszak, M.1
  • 32
    • 0002700949 scopus 로고
    • On the Local Geometry of a Bi-Hamiltonian Structure
    • Corwin L., (ed), Boston: Birkauser
    • Gel’fand, I.M., and Zakharevich, I., 1993. “On the Local Geometry of a Bi-Hamiltonian Structure”. In Gelfand Mathematical Seminars 1990–1992, Edited by:Corwin, L., 51–112. Boston:Birkauser.
    • (1993) Gelfand Mathematical Seminars 1990–1992 , pp. 51-112
    • Gel’fand, I.M.1    Zakharevich, I.2
  • 33
    • 0000757211 scopus 로고
    • Reduction of Poisson Manifolds
    • Marsden, J.E., and Ratiu, T., 1986. Reduction of Poisson Manifolds. Lett. Math. Phys., 11:161
    • (1986) Lett. Math. Phys. , vol.11 , pp. 161
    • Marsden, J.E.1    Ratiu, T.2
  • 34
    • 0001480249 scopus 로고
    • Bihamiltonian Manifolds and τ-Function
    • Gotay M.J., (ed), American Mathematical Society, Contemporary Mathematics
    • Casati, P., Magri, F., and Pedroni, M., 1992. “Bihamiltonian Manifolds and τ-Function”. In Mathematical Aspects of Classical Field Theory 1991, Edited by:Gotay, M. J., Vol. 132, 213–234. American Mathematical Society. Contemporary Mathematics
    • (1992) Mathematical Aspects of Classical Field Theory 1991 , vol.132 , pp. 213-234
    • Casati, P.1    Magri, F.2    Pedroni, M.3
  • 37
    • 0031582157 scopus 로고    scopus 로고
    • Quasi-Bi-Hamiltonian Systems and Separability
    • Morosi, C., and Tondo, G., 1997. Quasi-Bi-Hamiltonian Systems and Separability. J. Phys. A:Gen. Math., 30:2799
    • (1997) J. Phys. A: Gen. Math. , vol.30 , pp. 2799
    • Morosi, C.1    Tondo, G.2
  • 38
    • 0002629640 scopus 로고    scopus 로고
    • On a Class of Systems Both Quasi-Bi-Hamiltonian and Bi-Hamiltonian
    • Morosi, C., and Tondo, G., 1998. On a Class of Systems Both Quasi-Bi-Hamiltonian and Bi-Hamiltonian. Phys. Lett. A, 247:59
    • (1998) Phys. Lett. A , vol.247 , pp. 59
    • Morosi, C.1    Tondo, G.2
  • 39
    • 0033177375 scopus 로고    scopus 로고
    • Bi-Hamiltonian Manifolds, Quasi-Bi-Hamiltonian Systems and Separation of Variables
    • Tondo, G., and Morosi, C., 1999. Bi-Hamiltonian Manifolds, Quasi-Bi-Hamiltonian Systems and Separation of Variables. Rep. Math. Phys., 44
    • (1999) Rep. Math. Phys. , vol.44
    • Tondo, G.1    Morosi, C.2
  • 40
    • 0002021070 scopus 로고    scopus 로고
    • Some Developments of the Concepts of Poisson Manifolds in the Sense of A. Lichnerowicz
    • Ferrarese G., (ed), Bologna: Pitagora editrice
    • Magri, F., and Marsico, T., 1996. “Some Developments of the Concepts of Poisson Manifolds in the Sense of A. Lichnerowicz”. In Gravitation, Electromagnetism and Geometric Structures, Edited by:Ferrarese, G., 207Bologna:Pitagora editrice.
    • (1996) Gravitation, Electromagnetism and Geometric Structures , pp. 207
    • Magri, F.1    Marsico, T.2
  • 41
    • 0034348926 scopus 로고    scopus 로고
    • Reduction of Bihamiltonian Systems and Separation of Variables: An Example From the Boussinesq Hierarchy
    • press
    • Falqui, G., Magri, F., and Tondo, G., 2000. Reduction of Bihamiltonian Systems and Separation of Variables:An Example From the Boussinesq Hierarchy. Theor. Math. Phys., in press
    • (2000) Theor. Math. Phys.
    • Falqui, G.1    Magri, F.2    Tondo, G.3
  • 42
    • 0002274117 scopus 로고
    • On a Non-Standard Algebraic Description of Integrable Nonlinear Systems
    • Błaszak, M., 1993. On a Non-Standard Algebraic Description of Integrable Nonlinear Systems. Physica, 1988:637
    • (1993) Physica , vol.1988 , pp. 637
    • Błaszak, M.1
  • 43
    • 14944363471 scopus 로고
    • A New Class of Integrable Systems and its Relation to Solitons
    • Ruijsenaars, S.N., and Schneider, H., 1986. A New Class of Integrable Systems and its Relation to Solitons. Ann. Phys., 170:370
    • (1986) Ann. Phys. , vol.170 , pp. 370
    • Ruijsenaars, S.N.1    Schneider, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.