메뉴 건너뛰기




Volumn 38, Issue 12, 1997, Pages 6578-6602

Intrinsic characterization of the variable separation in the Hamilton-Jacobi equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0031530863     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532226     Document Type: Article
Times cited : (142)

References (42)
  • 1
    • 0000596484 scopus 로고
    • Über die Bewegung eines Punktes in einer n-fachen Mannigfaltigkeit
    • P. Stäckel, "Über die Bewegung eines Punktes in einer n-fachen Mannigfaltigkeit," Math. Ann. 42, 537 (1893); "Über quadratische Integrale der Differentialgleichungen der Dynamik," Ann. Math. Pure Appl. 26, 55 (1897).
    • (1893) Math. Ann. , vol.42 , pp. 537
    • Stäckel, P.1
  • 2
    • 51649215336 scopus 로고
    • Über quadratische Integrale der Differentialgleichungen der Dynamik
    • P. Stäckel, "Über die Bewegung eines Punktes in einer n-fachen Mannigfaltigkeit," Math. Ann. 42, 537 (1893); "Über quadratische Integrale der Differentialgleichungen der Dynamik," Ann. Math. Pure Appl. 26, 55 (1897).
    • (1897) Ann. Math. Pure Appl. , vol.26 , pp. 55
  • 3
    • 0000634574 scopus 로고
    • Sulla integrazione della equazione di Hamilton-Jacobi per separazione di variabili
    • T. Levi-Civita, "Sulla integrazione della equazione di Hamilton-Jacobi per separazione di variabili," Math. Ann. 59, 383 (1904).
    • (1904) Math. Ann. , vol.59 , pp. 383
    • Levi-Civita, T.1
  • 4
    • 0347671236 scopus 로고
    • Sulla integrazione delle equazioni di Hamilton-Jacobi per separazione delle variabili
    • F. A. Dall'Acqua, "Sulla integrazione delle equazioni di Hamilton-Jacobi per separazione delle variabili," Math. Ann. 66, 398 (1908).
    • (1908) Math. Ann. , vol.66 , pp. 398
    • DalL'Acqua, F.A.1
  • 5
    • 0345779096 scopus 로고
    • Sopra l'integrazione per separazione di variabili dell'equazione dinamica di Hamilton-Jacobi
    • C. Agostinelli, "Sopra l'integrazione per separazione di variabili dell'equazione dinamica di Hamilton-Jacobi," Mem. Acc. Scienze Torino 15, 3 (1937).
    • (1937) Mem. Acc. Scienze Torino , vol.15 , pp. 3
    • Agostinelli, C.1
  • 6
    • 84856124221 scopus 로고
    • Sur la séparation des variables dans l'équation de Hamilton-Jacobi d'un système nonconservatif
    • N. Forbat, "Sur la séparation des variables dans l'équation de Hamilton-Jacobi d'un système nonconservatif," Bull. Acad. R. Belg. 31, 462 (1944).
    • (1944) Bull. Acad. R. Belg. , vol.31 , pp. 462
    • Forbat, N.1
  • 7
    • 0007314587 scopus 로고
    • Integration of the Hamilton-Jacobi equation by the methods of separation of variables
    • M. S. Iarov-Iarovoi, "Integration of the Hamilton-Jacobi equation by the methods of separation of variables," J. Appl. Math. Mech. 27, 1499 (1963).
    • (1963) J. Appl. Math. Mech. , vol.27 , pp. 1499
    • Iarov-Iarovoi, M.S.1
  • 8
    • 0347671237 scopus 로고
    • Separation of variables in the Hamilton-Jacobi, Schrödinger end related equations. I-Complete separation. II-Partial separation
    • P. Havas, "Separation of variables in the Hamilton-Jacobi, Schrödinger end related equations. I-Complete separation. II-Partial separation," J. Math. Phys. 16, 1461, 2476 (1975).
    • (1975) J. Math. Phys. , vol.16 , pp. 1461
    • Havas, P.1
  • 9
    • 0007317466 scopus 로고
    • Separation of variables in the Hamilton-Jacobi equation for non-conservative systems
    • F. Cantrijn, "Separation of variables in the Hamilton-Jacobi equation for non-conservative systems," J. Phys. A 10, 491 (1977).
    • (1977) J. Phys. A , vol.10 , pp. 491
    • Cantrijn, F.1
  • 10
    • 0001682150 scopus 로고
    • Separability structures on Riemannian manifolds
    • S. Benenti, "Separability structures on Riemannian manifolds," Lect. Notes 2 Math. 863, 512 (1980).
    • (1980) Lect. Notes 2 Math. , vol.863 , pp. 512
    • Benenti, S.1
  • 11
    • 0002085496 scopus 로고
    • Separation of variables in the geodesic Hamilton-Jacobi equation
    • S. Benenti, "Separation of variables in the geodesic Hamilton-Jacobi equation," Prog. Math. Birkhäuser 9, 1 (1991).
    • (1991) Prog. Math. Birkhäuser , vol.9 , pp. 1
    • Benenti, S.1
  • 12
    • 0007255547 scopus 로고
    • Separability structures corresponding to conservative dynamical systems
    • S. Benenti and G. Pidello, "Separability structures corresponding to conservative dynamical systems," Meccanica 19, 275 (1984).
    • (1984) Meccanica , vol.19 , pp. 275
    • Benenti, S.1    Pidello, G.2
  • 13
    • 0001033506 scopus 로고
    • Separable systems of Stäckel
    • L. P. Eisenhart, "Separable systems of Stäckel," Ann. Math. 35, 284 (1934); Riemannian Geometry (Princeton University Press, 1949).
    • (1934) Ann. Math. , vol.35 , pp. 284
    • Eisenhart, L.P.1
  • 14
    • 0003439976 scopus 로고
    • Princeton University Press
    • L. P. Eisenhart, "Separable systems of Stäckel," Ann. Math. 35, 284 (1934); Riemannian Geometry (Princeton University Press, 1949).
    • (1949) Riemannian Geometry
  • 15
    • 0000742846 scopus 로고
    • Killing tensors and variable separation for Hamilton-Jacobi and Helmholtz equations
    • SIAM (Soc. Ind. Appl. Math.)
    • E. G. Kalnins and W. Miller, Jr., "Killing tensors and variable separation for Hamilton-Jacobi and Helmholtz equations," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 11, 1011 (1980).
    • (1980) J. Math. Anal. , vol.11 , pp. 1011
    • Kalnins, E.G.1    Miller W., Jr.2
  • 17
    • 0001777368 scopus 로고
    • Killing tensors and the separation of the Hamilton-Jacobi equation
    • N. M. J. Woodhouse, "Killing tensors and the separation of the Hamilton-Jacobi equation," Commun. Math. Phys. 44, 9 (1975).
    • (1975) Commun. Math. Phys. , vol.44 , pp. 9
    • Woodhouse, N.M.J.1
  • 18
    • 0002220473 scopus 로고
    • The theory of separability of the Hamillon-Jacobi equation and its applications to general relativity
    • edited by A. Held Plenum, New York
    • S. Benenti and M. Francaviglia, "The theory of separability of the Hamillon-Jacobi equation and its applications to general relativity," in General Relativity and Gravitation, edited by A. Held (Plenum, New York, 1980), Vol. 1, p. 393.
    • (1980) General Relativity and Gravitation , vol.1 , pp. 393
    • Benenti, S.1    Francaviglia, M.2
  • 19
    • 0007250761 scopus 로고
    • Intrinsic characterization or orthogonal separation of one coordinate in the Hamilton-Jacobi equation
    • E. G. Kalnins and W. Miller, Jr., "Intrinsic characterization or orthogonal separation of one coordinate in the Hamilton-Jacobi equation," J. Phys. A 15, 2003 (1982).
    • (1982) J. Phys. A , vol.15 , pp. 2003
    • Kalnins, E.G.1    Miller W., Jr.2
  • 20
    • 0000939046 scopus 로고
    • Killing tensors and nonorthogonal variable separation for Hamilton-Jacobi equations
    • SIAM (Soc. Ind. Appl. Math.)
    • E. G. Kalnins and W. Miller, Jr., "Killing tensors and nonorthogonal variable separation for Hamilton-Jacobi equations," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 12, 617 (1981).
    • (1981) J. Math. Anal. , vol.12 , pp. 617
    • Kalnins, E.G.1    Miller W., Jr.2
  • 21
    • 0005158482 scopus 로고
    • Mechanism for variable separation in partial differential equations and their relationship to group theory
    • World Scientific, Singapore
    • W. Miller Jr., "Mechanism for variable separation in partial differential equations and their relationship to group theory," in Symmetry and Nonlinear Phenomena (World Scientific, Singapore, 1988), p. 188.
    • (1988) Symmetry and Nonlinear Phenomena , pp. 188
    • Miller W., Jr.1
  • 22
    • 0011427161 scopus 로고
    • Bermerkung über separierbare Systeme in der Wellenmechanik
    • H. P. Robertson, "Bermerkung über separierbare Systeme in der Wellenmechanik," Math. Ann. 98, 749 (1927).
    • (1927) Math. Ann. , vol.98 , pp. 749
    • Robertson, H.P.1
  • 23
    • 0000314759 scopus 로고
    • Orthogonal separable dynamical systems
    • Differential Geometry and Its Applications, August 24-28, 1992 Silesian University, Opava
    • S. Benenti, "Orthogonal separable dynamical systems," in Differential Geometry and Its Applications, in Proceedings on the Conference in Opava (Czechoslovakia), August 24-28, 1992 (Silesian University, Opava, Vol. I, 1993), p. 163. Electronic edition: ELibEMS, http://www.emis.de/proceedings/.
    • (1993) Proceedings on the Conference in Opava (Czechoslovakia) , vol.1 , pp. 163
    • Benenti, S.1
  • 24
    • 0000646930 scopus 로고
    • Inertia tensors and Stäckel systems in the Euclidean spaces
    • S. Benenti, "Inertia tensors and Stäckel systems in the Euclidean spaces," Rend. Semin. Mat. Univ. Polit. Torino 50, 315 (1992).
    • (1992) Rend. Semin. Mat. Univ. Polit. Torino , vol.50 , pp. 315
    • Benenti, S.1
  • 25
    • 1642600178 scopus 로고
    • Singular points of the orthogonal separable coordinates in the hyperbolic plane
    • G. Rastelli, "Singular points of the orthogonal separable coordinates in the hyperbolic plane," Rend. Semin. Mat. Univ. Polit. Torino 52, 407 (1994).
    • (1994) Rend. Semin. Mat. Univ. Polit. Torino , vol.52 , pp. 407
    • Rastelli, G.1
  • 26
    • 0001631767 scopus 로고
    • Dynamical trajectories and geodesies
    • L. P. Eisenhart, "Dynamical trajectories and geodesies," Ann. Math. 30, 591 (1929).
    • (1929) Ann. Math. , vol.30 , pp. 591
    • Eisenhart, L.P.1
  • 27
    • 0007250684 scopus 로고
    • Orthogonal separation of variables on manifolds with constant curvature
    • S. Benenti, "Orthogonal separation of variables on manifolds with constant curvature," Diff. Geom. Appl. 2, 351 (1992).
    • (1992) Diff. Geom. Appl. , vol.2 , pp. 351
    • Benenti, S.1
  • 28
    • 85033151261 scopus 로고
    • University of Waikato Research Report No. 103
    • n," University of Waikato Research Report No. 105, 1984.
    • (1984) n
    • Kalnins, E.G.1    Miller W., Jr.2
  • 29
    • 85033156421 scopus 로고
    • University of Waikato Research Report No. 105
    • n," University of Waikato Research Report No. 105, 1984.
    • (1984) n
  • 31
    • 0003304757 scopus 로고
    • Separation of Variables for Riemannian Spaces of Constant Curvature
    • E. G. Kalnins, "Separation of Variables for Riemannian Spaces of Constant Curvature," Pitman Monographs 28 (1986).
    • (1986) Pitman Monographs , vol.28
    • Kalnins, E.G.1
  • 33
    • 0007178283 scopus 로고
    • When is a Hamiltonian system integrable?
    • I. Marshall and S. Wojciechowski, "When is a Hamiltonian system integrable?," J. Math. Phys. 29, 1338 (1988).
    • (1988) J. Math. Phys. , vol.29 , pp. 1338
    • Marshall, I.1    Wojciechowski, S.2
  • 34
    • 0040911334 scopus 로고
    • The complete Whittaker theorem for two-dimensional integrable systems and its applications
    • A. Ankiewicz and C. Pask, "The complete Whittaker theorem for two-dimensional integrable systems and its applications," J. Phys. A 16, 4203 (1983).
    • (1983) J. Phys. A , vol.16 , pp. 4203
    • Ankiewicz, A.1    Pask, C.2
  • 35
    • 36449007692 scopus 로고
    • Separability and Lax pairs for Henon-Heiles system
    • V. Ravoson, L. Gavrilov, and R. Caboz, "Separability and Lax pairs for Henon-Heiles system," J. Math. Phys. 34, 2385 (1993).
    • (1993) J. Math. Phys. , vol.34 , pp. 2385
    • Ravoson, V.1    Gavrilov, L.2    Caboz, R.3
  • 36
    • 0039824701 scopus 로고
    • Über die bedingt-periodische Bewegung eines Massenpunktes
    • J. Weinacht, "Über die bedingt-periodische Bewegung eines Massenpunktes," Math. Ann. 91, 279 (1923).
    • (1923) Math. Ann. , vol.91 , pp. 279
    • Weinacht, J.1
  • 37
    • 0347671236 scopus 로고
    • Sulla integrazione delle equazioni di Hamilton-Jacobi per separazione delle variabili
    • F. A. Dall'Acqua, "Sulla integrazione delle equazioni di Hamilton-Jacobi per separazione delle variabili," Math. Ann. 66, 398 (1908).
    • (1908) Math. Ann. , vol.66 , pp. 398
    • DalL'Acqua, F.A.1
  • 39
    • 0001760422 scopus 로고
    • Hamilton-Jacobi and Schrödinger separable solutions of Einstein equations
    • B. Carter, "Hamilton-Jacobi and Schrödinger separable solutions of Einstein equations," Commun. Math. Phys. 10, 280 (1968).
    • (1968) Commun. Math. Phys. , vol.10 , pp. 280
    • Carter, B.1
  • 41
    • 33845249997 scopus 로고
    • Killing horizons and orthogonally transitive groups in space-times
    • B. Carter, "Killing horizons and orthogonally transitive groups in space-times," J. Math. Phys. 10, 70 (1969).
    • (1969) J. Math. Phys. , vol.10 , pp. 70
    • Carter, B.1
  • 42
    • 0011319617 scopus 로고
    • Separation of variables and symmetry operators for the neutrino and Dirac equations in the space-times admitting a two-parameter Abelian orthogonally transitive isometry group and a pair of shearfree geodesic null congruences
    • N. Kamran and R. G. McLenaghan, "Separation of variables and symmetry operators for the neutrino and Dirac equations in the space-times admitting a two-parameter Abelian orthogonally transitive isometry group and a pair of shearfree geodesic null congruences," J Math. Phys. 25, 1019 (1984).
    • (1984) J Math. Phys. , vol.25 , pp. 1019
    • Kamran, N.1    McLenaghan, R.G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.