메뉴 건너뛰기




Volumn 53, Issue 1, 1998, Pages 1-58

Systems of PDEs obtained from factorization in loop groups

Author keywords

Affine Lie algebras; Integrable systems of PDEs; Riemann Hilbert splitting

Indexed keywords


EID: 0039826449     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1005947719355     Document Type: Article
Times cited : (19)

References (29)
  • 1
    • 84891310274 scopus 로고
    • Breaking solitons in 2 + 1-dimensional integrable equations
    • Bogoyavlenskii, O. I.: Breaking solitons in 2 + 1-dimensional integrable equations, Russian Math. Surveys 45(4) (1990), 1-86.
    • (1990) Russian Math. Surveys , vol.45 , Issue.4 , pp. 1-86
    • Bogoyavlenskii, O.I.1
  • 2
    • 56249128025 scopus 로고
    • N-soliton solutions of model equations for Shallow water waves
    • Hirota, R. and Satsuma, J.: N-soliton solutions of model equations for Shallow water waves, J. Phys. Soc. Japan 40 (1976), 611.
    • (1976) J. Phys. Soc. Japan , vol.40 , pp. 611
    • Hirota, R.1    Satsuma, J.2
  • 3
    • 34250120087 scopus 로고
    • Lie algebras and equations of Korteweg-deVries type
    • Drinfel'd, V. G. and Sokolov, V. V.: Lie algebras and equations of Korteweg-deVries type, J. Soviet Math. 30 (1985), 1975-2036.
    • (1985) J. Soviet Math. , vol.30 , pp. 1975-2036
    • Drinfel'd, V.G.1    Sokolov, V.V.2
  • 4
    • 21244460720 scopus 로고
    • The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebras
    • Wilson, G.: The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebras, Ergodic Theory Dynamical Systems 1 (1981), 361-380.
    • (1981) Ergodic Theory Dynamical Systems , vol.1 , pp. 361-380
    • Wilson, G.1
  • 5
    • 0001841091 scopus 로고
    • Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds
    • Sato M.: Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds, RIMS Kokyuroku 439 (1981), 30-46
    • (1981) RIMS Kokyuroku , vol.439 , pp. 30-46
    • Sato, M.1
  • 6
    • 0002472889 scopus 로고
    • Loop groups and equations of KdV type
    • Segal, G. and Wilson, G.: Loop groups and equations of KdV type, Publ. Math. IHES 63, (1984), 1-95.
    • (1984) Publ. Math. IHES , vol.63 , pp. 1-95
    • Segal, G.1    Wilson, G.2
  • 7
    • 51649165932 scopus 로고
    • The arithmetic theory of loop groups
    • Garland, H.: The arithmetic theory of loop groups, Publ. Math. IHES 52 (1980), 5-136.
    • (1980) Publ. Math. IHES , vol.52 , pp. 5-136
    • Garland, H.1
  • 8
    • 0000148293 scopus 로고
    • Infinite flag varieties and conjugacy theorems
    • Peterson, D. H. and Kac, V. G.: Infinite flag varieties and conjugacy theorems, Proc. Nat. Acad. Sci. USA 80 (1983), 1778-1782.
    • (1983) Proc. Nat. Acad. Sci. USA , vol.80 , pp. 1778-1782
    • Peterson, D.H.1    Kac, V.G.2
  • 9
    • 22344442192 scopus 로고
    • Collège de France, Paris
    • Tits, J.: Resumé de cours, Collège de France, Paris, 1981.
    • (1981) Resumé de Cours
    • Tits, J.1
  • 11
    • 84961471239 scopus 로고
    • Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle
    • Goodman, R. and Wallach, N. R.: Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle, J. Reine Angew. Math. 347 (1984), 69-133.
    • (1984) J. Reine Angew. Math. , vol.347 , pp. 69-133
    • Goodman, R.1    Wallach, N.R.2
  • 15
    • 84961469272 scopus 로고
    • Constant mean curvature surfaces and loop groups
    • Dorfmeister, J. and Wu, H.: Constant mean curvature surfaces and loop groups, J. Reine Angew. Math. 440 (1993), 43-76.
    • (1993) J. Reine Angew. Math. , vol.440 , pp. 43-76
    • Dorfmeister, J.1    Wu, H.2
  • 17
    • 25444503845 scopus 로고    scopus 로고
    • On constant mean curvature surfaces with periodic metric
    • to appear
    • Dorfmeister, J. and Haak, G.: On constant mean curvature surfaces with periodic metric, to appear in Pacific J. Math.
    • Pacific J. Math.
    • Dorfmeister, J.1    Haak, G.2
  • 18
    • 38249000988 scopus 로고
    • On the soliton content of the self dual Yang-Mills equations
    • Szmigielski, J.: On the soliton content of the self dual Yang-Mills equations, Phys. Lett. A 183 (1993), 293-300.
    • (1993) Phys. Lett. A , vol.183 , pp. 293-300
    • Szmigielski, J.1
  • 19
    • 0009218052 scopus 로고
    • Banach manifolds of solutions to nonlinear partial differential equations, and relations with finite-dimensional manifolds
    • Dorfmeister, J.: Banach manifolds of solutions to nonlinear partial differential equations, and relations with finite-dimensional manifolds, Proc. Sympos. Pure Math. 54 (1993), 121-139.
    • (1993) Proc. Sympos. Pure Math. , vol.54 , pp. 121-139
    • Dorfmeister, J.1
  • 21
    • 21144479741 scopus 로고
    • Generalized Drinfeld-Sokolov hierarchies. II. The Hamiltonian structures
    • Burroughs, N. J., de Groot, M. F., Hollowood, T. J., and Miramontes, J. L.: Generalized Drinfeld-Sokolov hierarchies. II. The Hamiltonian structures, Comm. Math. Phys. 153(1) (1993), 187-215.
    • (1993) Comm. Math. Phys. , vol.153 , Issue.1 , pp. 187-215
    • Burroughs, N.J.1    De Groot, M.F.2    Hollowood, T.J.3    Miramontes, J.L.4
  • 22
    • 21144461431 scopus 로고
    • Generalized Drinfeld-Sokolov reductions and KdV type hierarchies
    • Fehèr, L., Harnad, J., and Marshall, I.: Generalized Drinfeld-Sokolov reductions and KdV type hierarchies, Comm. Math. Phys. 154(1) (1993), 181-214.
    • (1993) Comm. Math. Phys. , vol.154 , Issue.1 , pp. 181-214
    • Fehèr, L.1    Harnad, J.2    Marshall, I.3
  • 23
    • 0004115280 scopus 로고
    • Ch. 1, Hermann, Paris, Ch. 2 et 3, Hermann, Paris, 1972; Ch. 4, 5 et 6, Hermann, Paris, 1968; Ch. 7 et 8, Hermann, Paris, 1975; Ch. 9, Masson, Paris
    • Bourbaki, B.: Groupes et algèbres de Lie. Ch. 1, Hermann, Paris, 1964; Ch. 2 et 3, Hermann, Paris, 1972; Ch. 4, 5 et 6, Hermann, Paris, 1968; Ch. 7 et 8, Hermann, Paris, 1975; Ch. 9, Masson, Paris, 1982.
    • (1964) Groupes et Algèbres de Lie
    • Bourbaki, B.1
  • 24
    • 0001511086 scopus 로고
    • Regular functions on certain infinite-dimensional groups
    • Progress in Math. 36, Birkhäuser, Boston
    • Kac, V G. and Peterson, D. K.: Regular functions on certain infinite-dimensional groups, in Arithmetic and Geometry, Progress in Math. 36, Birkhäuser, Boston, 1983, pp. 141-166.
    • (1983) Arithmetic and Geometry , pp. 141-166
    • Kac, V.G.1    Peterson, D.K.2
  • 27
    • 25444490208 scopus 로고    scopus 로고
    • A result on exponents of finite-dimensional simple Lie algebras and its application to Kac-Moody algebras
    • Gradl, H.: A result on exponents of finite-dimensional simple Lie algebras and its application to Kac-Moody algebras, Linear Algebra Appl. 233 (1996), 189-206.
    • (1996) Linear Algebra Appl. , vol.233 , pp. 189-206
    • Gradl, H.1
  • 28
    • 25144446408 scopus 로고
    • Factorization and the dressing method for the Gelfand-Dikii hierarchy
    • Sattinger, D. H. and Szmigielski, J.: Factorization and the dressing method for the Gelfand-Dikii hierarchy, Physica D 64 (1993), 1-34.
    • (1993) Physica D , vol.64 , pp. 1-34
    • Sattinger, D.H.1    Szmigielski, J.2
  • 29
    • 25444483420 scopus 로고    scopus 로고
    • Negative flows of the potential KP-hierarchy
    • Haak, G.: Negative flows of the potential KP-hierarchy, Trans. Amer. Math. Soc. 348(1) (1996), 375-390.
    • (1996) Trans. Amer. Math. Soc. , vol.348 , Issue.1 , pp. 375-390
    • Haak, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.