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Volumn 54, Issue 4, 2005, Pages 427-453

Deformations of semisimple bihamiltonian structures of hydrodynamic type

Author keywords

Bihamiltonian structure; Infinitesimal deformation; Poisson cohomology

Indexed keywords


EID: 19044364194     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2004.11.003     Document Type: Article
Times cited : (94)

References (30)
  • 1
    • 0035641135 scopus 로고    scopus 로고
    • The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDEs of shallow water and Dym type
    • M.S. Alber R. Camassa Yu.N. Fedorov D.D. Holm J.E. Marsden The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDEs of shallow water and Dym type Commun. Math. Phys. 221 2001 197-227
    • (2001) Commun. Math. Phys. , vol.221 , pp. 197-227
    • Alber, M.S.1    Camassa, R.2    Fedorov, Yu.N.3    Holm, D.D.4    Marsden, J.E.5
  • 2
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • R. Camassa D.D. Holm An integrable shallow water equation with peaked solitons Phys. Rev. Lett. 71 1993 1661-1664
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 4
    • 0010074217 scopus 로고
    • Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view
    • P. Casati M. Pedroni Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view Lett. Math. Phys. 25 1992 89-101
    • (1992) Lett. Math. Phys. , vol.25 , pp. 89-101
    • Casati, P.1    Pedroni, M.2
  • 5
    • 19044377881 scopus 로고    scopus 로고
    • The extended Toda hierarchy
    • nlin-SI/0306060
    • G. Carlet, B. Dubrovin, Y. Zhang, The extended Toda hierarchy, nlin-SI/ 0306060, Moscow Math. J. 4 (2) (2004) 313.
    • (2004) Moscow Math. J. , vol.4 , Issue.2 , pp. 313
    • Carlet, G.1    Dubrovin, B.2    Zhang, Y.3
  • 6
    • 0001627817 scopus 로고
    • Spectral sequences and the inverse problem of the calculus of variations
    • P. Dedecker W.M. Tulczyjev Spectral sequences and the inverse problem of the calculus of variations Lecture Notes Math. 836 1980 498-503
    • (1980) Lecture Notes Math. , vol.836 , pp. 498-503
    • Dedecker, P.1    Tulczyjev, W.M.2
  • 7
    • 11244325832 scopus 로고    scopus 로고
    • On deformation of Poisson manifolds of hydrodynamic type
    • nlin.SI/010352
    • L. Degiovanni, F. Magri, V. Sciacca, On deformation of Poisson manifolds of hydrodynamic type. nlin.SI/010352.
    • Degiovanni, L.1    Magri, F.2    Sciacca, V.3
  • 9
    • 0000644797 scopus 로고    scopus 로고
    • Geometry of 2D topological field theories
    • M. Francaviglia, S. Greco (Eds.), Integrable Systems and Quantum Groups, Montecatini, Terme 1993
    • B. Dubrovin, Geometry of 2D topological field theories, in: M. Francaviglia, S. Greco (Eds.), Integrable Systems and Quantum Groups, Montecatini, Terme, 1993. Springer Lecture Notes in Mathematics 1620 (1996) 120-348.
    • (1996) Springer Lecture Notes in Mathematics , vol.1620 , pp. 120-348
    • Dubrovin, B.1
  • 10
    • 0001392731 scopus 로고
    • The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method
    • B. Dubrovin S.P. Novikov The Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method Sov. Math. Dokl. 270 4 1983 665-669
    • (1983) Sov. Math. Dokl. , vol.270 , Issue.4 , pp. 665-669
    • Dubrovin, B.1    Novikov, S.P.2
  • 11
    • 0006666175 scopus 로고
    • On Poisson brackets of hydrodynamic type
    • B. Dubrovin S.P. Novikov On Poisson brackets of hydrodynamic type Sov. Math. Dokl. 279 2 1984 294-297
    • (1984) Sov. Math. Dokl. , vol.279 , Issue.2 , pp. 294-297
    • Dubrovin, B.1    Novikov, S.P.2
  • 12
    • 0347767249 scopus 로고
    • Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
    • B. Dubrovin S.P. Novikov Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory Russ. Math. Surv. 44 1989 35-124
    • (1989) Russ. Math. Surv. , vol.44 , pp. 35-124
    • Dubrovin, B.1    Novikov, S.P.2
  • 13
    • 0032276702 scopus 로고    scopus 로고
    • Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation
    • B. Dubrovin Y. Zhang Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation Commun. Math. Phys. 198 1998 311-361
    • (1998) Commun. Math. Phys. , vol.198 , pp. 311-361
    • Dubrovin, B.1    Zhang, Y.2
  • 14
    • 0012863387 scopus 로고    scopus 로고
    • Normal forms of integrable PDEs, Frobenius manifolds and Gromov-Witten invariants
    • math.DG/0108160
    • B. Dubrovin, Y. Zhang, Normal forms of integrable PDEs, Frobenius manifolds and Gromov-Witten invariants. math.DG/0108160.
    • Dubrovin, B.1    Zhang, Y.2
  • 15
    • 4744344138 scopus 로고    scopus 로고
    • Virasoro symmetries of the extended Toda hierarchy
    • math.DG/0308152
    • B. Dubrovin, Y. Zhang, Virasoro symmetries of the extended Toda hierarchy, math.DG/0308152, Commun. Math. Phys. 250 (2004) 161-193.
    • (2004) Commun. Math. Phys. , vol.250 , pp. 161-193
    • Dubrovin, B.1    Zhang, Y.2
  • 16
    • 0000204750 scopus 로고
    • On the genus expansion in the topological string theory
    • T. Eguchi Y. Yamada S.-K. Yang On the genus expansion in the topological string theory Rev. Math. Phys. 7 1995 279-309
    • (1995) Rev. Math. Phys. , vol.7 , pp. 279-309
    • Eguchi, T.1    Yamada, Y.2    Yang, S.-K.3
  • 17
    • 0035937671 scopus 로고    scopus 로고
    • Compatible Poisson brackets of hydrodynamic type
    • E.V. Ferapontov Compatible Poisson brackets of hydrodynamic type J. Phys. A 34 11 2001 2377-2388
    • (2001) J. Phys. A , vol.34 , Issue.11 , pp. 2377-2388
    • Ferapontov, E.V.1
  • 18
    • 0001702502 scopus 로고
    • On a class of physically important integrable equations
    • A.S. Fokas On a class of physically important integrable equations Physica D 87 1995 145-150
    • (1995) Physica D , vol.87 , pp. 145-150
    • Fokas, A.S.1
  • 19
    • 22244482803 scopus 로고    scopus 로고
    • Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
    • B. Fuchssteiner Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation Physica D 95 1996 229-243
    • (1996) Physica D , vol.95 , pp. 229-243
    • Fuchssteiner, B.1
  • 20
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • B. Fuchssteiner A.S. Fokas Symplectic structures, their Bäcklund transformations and hereditary symmetries Physica D 4 1981 47-66
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 21
    • 36849102552 scopus 로고
    • Korteweg-de Vries equation and generalizations IV
    • C.S. Gardner Korteweg-de Vries equation and generalizations IV J. Math. Phys. 12 1971 1548-1551
    • (1971) J. Math. Phys. , vol.12 , pp. 1548-1551
    • Gardner, C.S.1
  • 22
    • 0037085530 scopus 로고    scopus 로고
    • A Darboux theorem for Hamiltonian operators in the formal calculus of variations
    • E. Getzler A Darboux theorem for Hamiltonian operators in the formal calculus of variations Duke Math. J. 111 2002 535-560
    • (2002) Duke Math. J. , vol.111 , pp. 535-560
    • Getzler, E.1
  • 23
    • 0041997524 scopus 로고    scopus 로고
    • The Toda conjecture
    • (Seoul, 2000) World Scientific Publishing River Edge, NJ math.AG/0108108
    • E. Getzler The Toda conjecture Symplectic Geometry and Mirror Symmetry (Seoul, 2000) 2001 World Scientific Publishing River Edge, NJ 51-79 math.AG/0108108
    • (2001) Symplectic Geometry and Mirror Symmetry , pp. 51-79
    • Getzler, E.1
  • 24
    • 84972540666 scopus 로고
    • Les varietes de Poisson et leurs algèbres de Lie associeés
    • A. Lichnerowicz Les varietes de Poisson et leurs algèbres de Lie associeés J. Diff. Geom. 12 1977 253-300
    • (1977) J. Diff. Geom. , vol.12 , pp. 253-300
    • Lichnerowicz, A.1
  • 25
    • 0036888090 scopus 로고    scopus 로고
    • Deformations of bihamiltonian structures of hydrodynamic type
    • P. Lorenzoni Deformations of bihamiltonian structures of hydrodynamic type J. Geom. Phys. 44 2002 331-375
    • (2002) J. Geom. Phys. , vol.44 , pp. 331-375
    • Lorenzoni, P.1
  • 26
    • 12844252460 scopus 로고    scopus 로고
    • The conservation of the Hamiltonian structures in Whitham's method of averaging, Izvestiya
    • A. Maltsev The conservation of the Hamiltonian structures in Whitham's method of averaging, Izvestiya Mathematics 63 6 1999 1171-1201
    • (1999) Mathematics , vol.63 , Issue.6 , pp. 1171-1201
    • Maltsev, A.1
  • 27
    • 0001666846 scopus 로고
    • A simple construction of integrable systems
    • F. Magri A simple construction of integrable systems J. Math. Phys. 19 1978 1156-1162
    • (1978) J. Math. Phys. , vol.19 , pp. 1156-1162
    • Magri, F.1
  • 28
    • 0035619225 scopus 로고    scopus 로고
    • Compatible and almost compatible pseudo-Riemannian metrics
    • O.I. Mokhov Compatible and almost compatible pseudo-Riemannian metrics Funct. Anal. Appl. 35 2 2001 100-110
    • (2001) Funct. Anal. Appl. , vol.35 , Issue.2 , pp. 100-110
    • Mokhov, O.I.1
  • 29
    • 0002161530 scopus 로고
    • Korteweg-de Vries equation is a completely integrable Hamiltonian system
    • V.E. Zakharov L.D. Faddeev Korteweg-de Vries equation is a completely integrable Hamiltonian system Funkz. Anal. Priloz. 5 1971 18-27
    • (1971) Funkz. Anal. Priloz. , vol.5 , pp. 18-27
    • Zakharov, V.E.1    Faddeev, L.D.2
  • 30
    • 0346532050 scopus 로고    scopus 로고
    • 1 topological sigma model and the Toda lattice hierarchy
    • 1 topological sigma model and the Toda lattice hierarchy J. Geom. Phys. 40 2002 215-232
    • (2002) J. Geom. Phys. , vol.40 , pp. 215-232
    • Zhang, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.