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Volumn 63, Issue 2, 2003, Pages 125-139

A note on the dispersionless Dym hierarchy

Author keywords

bi Hamiltonian structure; dispersionless Dym hierarchy; Landau Ginzburg formulation; Miura map

Indexed keywords


EID: 0142227379     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023082617759     Document Type: Article
Times cited : (19)

References (33)
  • 1
    • 0011602912 scopus 로고
    • Topological conformal field theory with a rational W potential and the dispersionless KP hierarchy
    • Aoyama, S. and Kodama, Y.: Topological conformal field theory with a rational W potential and the dispersionless KP hierarchy, Modern Phys. Lett. A 9 (1994), 2481-2491; Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy, Comm. Math. Phys. 182 (1996), 185-219.
    • (1994) Modern Phys. Lett. A , vol.9 , pp. 2481-2491
    • Aoyama, S.1    Kodama, Y.2
  • 2
    • 0000655552 scopus 로고    scopus 로고
    • Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
    • Aoyama, S. and Kodama, Y.: Topological conformal field theory with a rational W potential and the dispersionless KP hierarchy, Modern Phys. Lett. A 9 (1994), 2481-2491; Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy, Comm. Math. Phys. 182 (1996), 185-219.
    • (1996) Comm. Math. Phys. , vol.182 , pp. 185-219
  • 3
    • 0000730150 scopus 로고
    • R-matrix formulation of KP hierarchies and their gauge equivalence
    • Aratyn, H., Nissimov, E., Pacheva, S. and Vaysburd, I.: R-matrix formulation of KP hierarchies and their gauge equivalence, Phys. Lett. B 294 (1992), 167-176.
    • (1992) Phys. Lett. B , vol.294 , pp. 167-176
    • Aratyn, H.1    Nissimov, E.2    Pacheva, S.3    Vaysburd, I.4
  • 5
    • 0037071094 scopus 로고    scopus 로고
    • Classical R-matrices on Poisson algebras and related dispersionless systems
    • Blaszak, M.: Classical R-matrices on Poisson algebras and related dispersionless systems, Phys. Lett. A 297 (2002), 191-195.
    • (2002) Phys. Lett. A , vol.297 , pp. 191-195
    • Blaszak, M.1
  • 6
    • 0034336563 scopus 로고    scopus 로고
    • On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies
    • Chang, J. H. and Tu, M. H.: On the Miura map between the dispersionless KP and dispersionless modified KP hierarchies, J. Math. Phys. 41 (2000), 5391-5406.
    • (2000) J. Math. Phys. , vol.41 , pp. 5391-5406
    • Chang, J.H.1    Tu, M.H.2
  • 7
    • 0034355658 scopus 로고    scopus 로고
    • Poisson algebras associated with constrained dispersionless modified Kadomtsev-Petviashvili hierarchies
    • Chang, J. H. and Tu, M. H.: Poisson algebras associated with constrained dispersionless modified Kadomtsev-Petviashvili hierarchies, J. Math. Phys. 41 (2000), 8117-8131.
    • (2000) J. Math. Phys. , vol.41 , pp. 8117-8131
    • Chang, J.H.1    Tu, M.H.2
  • 8
    • 0035910684 scopus 로고    scopus 로고
    • On the Benney hierarchy: Free energy, string equation and quantization
    • Chang, J. H. and Tu, M. H.: On the Benney hierarchy: free energy, string equation and quantization, J. Phys. A 34 (2001), 251-272.
    • (2001) J. Phys. A , vol.34 , pp. 251-272
    • Chang, J.H.1    Tu, M.H.2
  • 10
    • 0000818276 scopus 로고
    • Mean field theory, topological field theory, and multi-matrix models
    • Dijkgraaf, R. and Witten, E.: Mean field theory, topological field theory, and multi-matrix models, Nuclear Phys. B 342 (1990), 486-522.
    • (1990) Nuclear Phys. B , vol.342 , pp. 486-522
    • Dijkgraaf, R.1    Witten, E.2
  • 11
    • 0347427534 scopus 로고
    • Integrable systems in topological field theory
    • Dubrovin, B.: Integrable systems in topological field theory, Nuclear Phys. B 379 (1992), 627-689.
    • (1992) Nuclear Phys. B , vol.379 , pp. 627-689
    • Dubrovin, B.1
  • 12
    • 0000644797 scopus 로고    scopus 로고
    • Geometry of 2D topological field theories
    • M. Francaviglia and S. Greco (eds), Springer, Berlin
    • Dubrovin, B.: Geometry of 2D topological field theories, In: M. Francaviglia and S. Greco (eds), Integrable Systems and Quantum Group, Springer, Berlin, 1996, pp. 120-348.
    • (1996) Integrable Systems and Quantum Group , pp. 120-348
    • Dubrovin, B.1
  • 13
    • 0001040308 scopus 로고
    • Poisson brackets of hydrodynamic type
    • Dubrovin, B. and Novikov, S. P.: Poisson brackets of hydrodynamic type, Soviet. Math. Dokl. 30 (1984), 651-654.
    • (1984) Soviet. Math. Dokl. , vol.30 , pp. 651-654
    • Dubrovin, B.1    Novikov, S.P.2
  • 14
    • 0032276702 scopus 로고    scopus 로고
    • Bi-Hamiltonian hierarchies in 2D topological field theory at one-loop approximation
    • Dubrovin, B. and Zhang, Y.: Bi-Hamiltonian hierarchies in 2D topological field theory at one-loop approximation, Comm. Math. Phys. 198 (1998), 311-361; Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov-Witten invariants, Preprint (math.DG/0108160).
    • (1998) Comm. Math. Phys. , vol.198 , pp. 311-361
    • Dubrovin, B.1    Zhang, Y.2
  • 15
    • 0032276702 scopus 로고    scopus 로고
    • Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov-Witten invariants, Preprint (math.DG/0108160)
    • Dubrovin, B. and Zhang, Y.: Bi-Hamiltonian hierarchies in 2D topological field theory at one-loop approximation, Comm. Math. Phys. 198 (1998), 311-361; Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov-Witten invariants, Preprint (math.DG/0108160).
  • 16
  • 17
    • 0001415486 scopus 로고    scopus 로고
    • The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies
    • Fairlie, D. B. and Strachan, I. A. B.: The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies, Inverse Problems 12 (1996), 885-908.
    • (1996) Inverse Problems , vol.12 , pp. 885-908
    • Fairlie, D.B.1    Strachan, I.A.B.2
  • 18
    • 34249927843 scopus 로고
    • Integrable equations related with the Poisson algebra
    • Golenischeva-Kutuzova, M. and Reiman, A. G.: Integrable equations related with the Poisson algebra, J. Soviet Math. 169 (1988), 890-894.
    • (1988) J. Soviet Math. , vol.169 , pp. 890-894
    • Golenischeva-Kutuzova, M.1    Reiman, A.G.2
  • 19
    • 0040056809 scopus 로고
    • Topological strings with scaling violation and Toda lattice hierarchy
    • Kanno, H. and Ohta, Y.: Topological strings with scaling violation and Toda lattice hierarchy, Nuclear. Phys. B 442 (1995), 179-201.
    • (1995) Nuclear. Phys. B , vol.442 , pp. 179-201
    • Kanno, H.1    Ohta, Y.2
  • 21
    • 85008031283 scopus 로고
    • An r-matrix approach to nonstandard classes of integrable equations
    • Konopelchenko, B. and Oevel, W.: An r-matrix approach to nonstandard classes of integrable equations, Publ. Res. Inst. Math. Sci. 29 (1993), 581-666.
    • (1993) Publ. Res. Inst. Math. Sci. , vol.29 , pp. 581-666
    • Konopelchenko, B.1    Oevel, W.2
  • 22
    • 0037512871 scopus 로고
    • The dispersionless Lax equations and topological minimal models
    • Krichever, I.: The dispersionless Lax equations and topological minimal models, Comm. Math. Phys. 143 (1992), 415-429.
    • (1992) Comm. Math. Phys. , vol.143 , pp. 415-429
    • Krichever, I.1
  • 23
    • 34250112720 scopus 로고
    • Mathematics of dispersive water waves
    • Kupershmidt, B.: Mathematics of dispersive water waves, Comm. Math. Phys. 99 (1985), 51-73.
    • (1985) Comm. Math. Phys. , vol.99 , pp. 51-73
    • Kupershmidt, B.1
  • 24
    • 0041823497 scopus 로고
    • The quasiclassical limit of the modified KP hierarchy
    • Kupershmidt, B.: The quasiclassical limit of the modified KP hierarchy, J. Phys. A 23 (1990), 871-886.
    • (1990) J. Phys. A , vol.23 , pp. 871-886
    • Kupershmidt, B.1
  • 25
    • 0001338252 scopus 로고
    • Conservation laws and Lax representation of Benney's long wave equations
    • Lebedev, D. R. and Manin, Yu. I.: Conservation laws and Lax representation of Benney's long wave equations, Phys. Lett. A 74 (1979), 154-156.
    • (1979) Phys. Lett. A , vol.74 , pp. 154-156
    • Lebedev, D.R.1    Manin, Yu.I.2
  • 26
    • 0033242956 scopus 로고    scopus 로고
    • Classical r-matrices and compatible Poisson structures for Lax equations on Poisson algebras
    • Li, L. C.: Classical r-matrices and compatible Poisson structures for Lax equations on Poisson algebras, Comm. Math. Phys. 203 (1999), 573-592.
    • (1999) Comm. Math. Phys. , vol.203 , pp. 573-592
    • Li, L.C.1
  • 27
    • 0001708223 scopus 로고
    • Gauge transformations and reciprocal links in 2 + 1 dimensions
    • Oevel, W. and Rogers, C.: Gauge transformations and reciprocal links in 2 + 1 dimensions, Rev. Math. Phys. 5 (1993), 299-330.
    • (1993) Rev. Math. Phys. , vol.5 , pp. 299-330
    • Oevel, W.1    Rogers, C.2
  • 29
    • 0001060060 scopus 로고
    • Integrable hierarchies and dispersionless limit
    • Takasaki, K. and Takebe, T.: Integrable hierarchies and dispersionless limit, Rev. Math. Phys. 7 (1995), 743-808.
    • (1995) Rev. Math. Phys. , vol.7 , pp. 743-808
    • Takasaki, K.1    Takebe, T.2
  • 30
    • 0001354012 scopus 로고
    • Quasi-classical limit of Toda hierarchy and W-infinity symmetries
    • Takasaki, K. and Takebe, T.: Quasi-classical limit of Toda hierarchy and W-infinity symmetries, Lett. Math. Phys. 28 (1993), 165-176.
    • (1993) Lett. Math. Phys. , vol.28 , pp. 165-176
    • Takasaki, K.1    Takebe, T.2
  • 31
    • 0000836475 scopus 로고
    • Topological Landau-Ginzburg models
    • Vafa, C.: Topological Landau-Ginzburg models, Modern Phys. Lett. A 6 (1991), 337-346.
    • (1991) Modern Phys. Lett. A , vol.6 , pp. 337-346
    • Vafa, C.1
  • 32
    • 36749110322 scopus 로고
    • The Painlevé property for partial differential equations. II: Backlund transformation, Lax pairs, and the Schwarzian derivative
    • Weiss, J.: The Painlevé property for partial differential equations. II: Backlund transformation, Lax pairs, and the Schwarzian derivative, J. Math. Phys. 24 (1983), 1405-1413.
    • (1983) J. Math. Phys. , vol.24 , pp. 1405-1413
    • Weiss, J.1
  • 33
    • 0009243741 scopus 로고
    • On the structure of the topological phase of two-dimensional gravity
    • Witten, E.: On the structure of the topological phase of two-dimensional gravity, Nuclear Phys. B 340 (1990), 281-332.
    • (1990) Nuclear Phys. B , vol.340 , pp. 281-332
    • Witten, E.1


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