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Volumn 316, Issue 1-2, 2003, Pages 77-83

Towards noncommutative integrable systems

Author keywords

[No Author keywords available]

Indexed keywords

DIMENSIONAL SPACES; INTEGRABILITY; INTEGRABLE EQUATIONS; INTEGRABLE SYSTEMS; LAX EQUATION; LAX REPRESENTATION; NON-COMMUTATIVE; YANG-MILLS EQUATION;

EID: 17544386162     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0375-9601(03)01138-1     Document Type: Article
Times cited : (72)

References (52)
  • 1
    • 0035486599 scopus 로고    scopus 로고
    • hep-th/0106048, and references therein
    • M.R. Douglas, N.A. Nekrasov, Rev. Mod. Phys. 73 (2002) 977, hep-th/0106048, and references therein.
    • (2002) Rev. Mod. Phys. , vol.73 , pp. 977
    • Douglas, M.R.1    Nekrasov, N.A.2
  • 2
    • 85031077730 scopus 로고    scopus 로고
    • hep-th/0102076, and references therein
    • J.A. Harvey, hep-th/0102076, and references therein.
    • Harvey, J.A.1
  • 5
    • 0035536783 scopus 로고    scopus 로고
    • hep-th/0002193
    • A. Kapustin, A. Kuznetsov, D. Orlov, Commun. Math. Phys. 221 (2001) 385, hep-th/0002193; K. Takasaki, J. Geom. Phys. 37 (2001) 291, hep-th/0005194; K.C. Hannabuss, Lett. Math. Phys. 58 (2001) 153, hep-th/0108228; O. Lechtenfeld, A.D. Popov, JHEP 0203 (2002) 040, hep-th/0109209; Z. Horváth, O. Lechtenfeld, M. Wolf, JHEP 0212 (2002) 060, hep-th/0211041.
    • (2001) Commun. Math. Phys. , vol.221 , pp. 385
    • Kapustin, A.1    Kuznetsov, A.2    Orlov, D.3
  • 6
    • 0039943307 scopus 로고    scopus 로고
    • hep-th/0005194
    • A. Kapustin, A. Kuznetsov, D. Orlov, Commun. Math. Phys. 221 (2001) 385, hep-th/0002193; K. Takasaki, J. Geom. Phys. 37 (2001) 291, hep-th/0005194; K.C. Hannabuss, Lett. Math. Phys. 58 (2001) 153, hep-th/0108228; O. Lechtenfeld, A.D. Popov, JHEP 0203 (2002) 040, hep-th/0109209; Z. Horváth, O. Lechtenfeld, M. Wolf, JHEP 0212 (2002) 060, hep-th/0211041.
    • (2001) J. Geom. Phys. , vol.37 , pp. 291
    • Takasaki, K.1
  • 7
    • 0039569247 scopus 로고    scopus 로고
    • hep-th/0108228
    • A. Kapustin, A. Kuznetsov, D. Orlov, Commun. Math. Phys. 221 (2001) 385, hep-th/0002193; K. Takasaki, J. Geom. Phys. 37 (2001) 291, hep-th/0005194; K.C. Hannabuss, Lett. Math. Phys. 58 (2001) 153, hep-th/0108228; O. Lechtenfeld, A.D. Popov, JHEP 0203 (2002) 040, hep-th/0109209; Z. Horváth, O. Lechtenfeld, M. Wolf, JHEP 0212 (2002) 060, hep-th/0211041.
    • (2001) Lett. Math. Phys. , vol.58 , pp. 153
    • Hannabuss, K.C.1
  • 8
    • 23044504662 scopus 로고    scopus 로고
    • hep-th/0109209
    • A. Kapustin, A. Kuznetsov, D. Orlov, Commun. Math. Phys. 221 (2001) 385, hep-th/0002193; K. Takasaki, J. Geom. Phys. 37 (2001) 291, hep-th/0005194; K.C. Hannabuss, Lett. Math. Phys. 58 (2001) 153, hep-th/0108228; O. Lechtenfeld, A.D. Popov, JHEP 0203 (2002) 040, hep-th/0109209; Z. Horváth, O. Lechtenfeld, M. Wolf, JHEP 0212 (2002) 060, hep-th/0211041.
    • (2002) JHEP , vol.203 , pp. 040
    • Lechtenfeld, O.1    Popov, A.D.2
  • 9
    • 21444439985 scopus 로고    scopus 로고
    • hep-th/0211041
    • A. Kapustin, A. Kuznetsov, D. Orlov, Commun. Math. Phys. 221 (2001) 385, hep-th/0002193; K. Takasaki, J. Geom. Phys. 37 (2001) 291, hep-th/0005194; K.C. Hannabuss, Lett. Math. Phys. 58 (2001) 153, hep-th/0108228; O. Lechtenfeld, A.D. Popov, JHEP 0203 (2002) 040, hep-th/0109209; Z. Horváth, O. Lechtenfeld, M. Wolf, JHEP 0212 (2002) 060, hep-th/0211041.
    • (2002) JHEP , vol.212 , pp. 060
    • Horváth, Z.1    Lechtenfeld, O.2    Wolf, M.3
  • 10
    • 85031080338 scopus 로고    scopus 로고
    • hep-th/0011095, and references therein
    • N.A. Nekrasov, hep-th/0011095, and references therein.
    • Nekrasov, N.A.1
  • 12
    • 0040435681 scopus 로고    scopus 로고
    • math-ph/9908015
    • A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 957, math-ph/ 9908015; A. Dimakis, F. Muller-Hoissen, Int. J. Mod. Phys. B 14 (2000) 2455, hep-th/0006005; A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 6579, nlin.si/0006029; A. Dimakis, F. Muller-Hoissen, hep-th/0007015; A. Dimakis, F. Muller-Hoissen, J. Phys. A 34 (2001) 9163, nlin.SI/0104071.
    • (2000) J. Phys. A , vol.33 , pp. 957
    • Dimakis, A.1    Muller-Hoissen, F.2
  • 13
    • 0034692276 scopus 로고    scopus 로고
    • hep-th/0006005
    • A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 957, math-ph/ 9908015; A. Dimakis, F. Muller-Hoissen, Int. J. Mod. Phys. B 14 (2000) 2455, hep-th/0006005; A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 6579, nlin.si/0006029; A. Dimakis, F. Muller-Hoissen, hep-th/0007015; A. Dimakis, F. Muller-Hoissen, J. Phys. A 34 (2001) 9163, nlin.SI/0104071.
    • (2000) Int. J. Mod. Phys. B , vol.14 , pp. 2455
    • Dimakis, A.1    Muller-Hoissen, F.2
  • 14
    • 0040435634 scopus 로고    scopus 로고
    • nlin.si/0006029
    • A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 957, math-ph/ 9908015; A. Dimakis, F. Muller-Hoissen, Int. J. Mod. Phys. B 14 (2000) 2455, hep-th/0006005; A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 6579, nlin.si/0006029; A. Dimakis, F. Muller-Hoissen, hep-th/0007015; A. Dimakis, F. Muller-Hoissen, J. Phys. A 34 (2001) 9163, nlin.SI/0104071.
    • (2000) J. Phys. A , vol.33 , pp. 6579
    • Dimakis, A.1    Muller-Hoissen, F.2
  • 15
    • 0040435681 scopus 로고    scopus 로고
    • A. Dimakis, F. Muller-Hoissen, hep-th/0007015
    • A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 957, math-ph/ 9908015; A. Dimakis, F. Muller-Hoissen, Int. J. Mod. Phys. B 14 (2000) 2455, hep-th/0006005; A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 6579, nlin.si/0006029; A. Dimakis, F. Muller-Hoissen, hep-th/0007015; A. Dimakis, F. Muller-Hoissen, J. Phys. A 34 (2001) 9163, nlin.SI/0104071.
  • 16
    • 0035798525 scopus 로고    scopus 로고
    • nlin.SI/0104071
    • A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 957, math-ph/ 9908015; A. Dimakis, F. Muller-Hoissen, Int. J. Mod. Phys. B 14 (2000) 2455, hep-th/0006005; A. Dimakis, F. Muller-Hoissen, J. Phys. A 33 (2000) 6579, nlin.si/0006029; A. Dimakis, F. Muller-Hoissen, hep-th/0007015; A. Dimakis, F. Muller-Hoissen, J. Phys. A 34 (2001) 9163, nlin.SI/0104071.
    • (2001) J. Phys. A , vol.34 , pp. 9163
    • Dimakis, A.1    Muller-Hoissen, F.2
  • 17
    • 85031072523 scopus 로고    scopus 로고
    • A. Dimakis, F. Muller-Hoissen, hep-th/0007074
    • A. Dimakis, F. Muller-Hoissen, hep-th/0007074.
  • 18
    • 85031074167 scopus 로고    scopus 로고
    • M.T. Grisaru, S. Penati, hep-th/0112246
    • M.T. Grisaru, S. Penati, hep-th/0112246.
  • 19
    • 0001437082 scopus 로고
    • R.S. Ward, Philos. Trans. R. Soc. London A 315 (1985) 451; R.S. Ward, Multidimensional integrable systems, in: Lecture Notes in Phys., Vol. 280, Springer, Berlin, 1986, p. 106; R.S. Ward, Integrable systems in twistor theory, in: Twistors in Mathematics and Physics, Cambridge Univ. Press, Cambridge, 1990, p. 246.
    • (1985) Philos. Trans. R. Soc. London A , vol.315 , pp. 451
    • Ward, R.S.1
  • 20
    • 0007470205 scopus 로고
    • Multidimensional integrable systems
    • Springer, Berlin
    • R.S. Ward, Philos. Trans. R. Soc. London A 315 (1985) 451; R.S. Ward, Multidimensional integrable systems, in: Lecture Notes in Phys., Vol. 280, Springer, Berlin, 1986, p. 106; R.S. Ward, Integrable systems in twistor theory, in: Twistors in Mathematics and Physics, Cambridge Univ. Press, Cambridge, 1990, p. 246.
    • (1986) Lecture Notes in Phys. , vol.280 , pp. 106
    • Ward, R.S.1
  • 21
    • 0000255752 scopus 로고
    • Integrable systems in twistor theory
    • Cambridge Univ. Press, Cambridge
    • R.S. Ward, Philos. Trans. R. Soc. London A 315 (1985) 451; R.S. Ward, Multidimensional integrable systems, in: Lecture Notes in Phys., Vol. 280, Springer, Berlin, 1986, p. 106; R.S. Ward, Integrable systems in twistor theory, in: Twistors in Mathematics and Physics, Cambridge Univ. Press, Cambridge, 1990, p. 246.
    • (1990) Twistors in Mathematics and Physics , pp. 246
    • Ward, R.S.1
  • 23
    • 0003402847 scopus 로고    scopus 로고
    • Oxford Univ. Press, Oxford, and references therein
    • M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge Univ. Press, Cambridge, 1991; L.J. Mason, N.M. Woodhouse, Integrability, Self-Duality, and Twistor Theory, Oxford Univ. Press, Oxford, 1996, and references therein.
    • (1996) Integrability, Self-Duality, and Twistor Theory
    • Mason, L.J.1    Woodhouse, N.M.2
  • 25
    • 85031074865 scopus 로고    scopus 로고
    • M. Legare, hep-th/0012077
    • M. Legare, hep-th/0012077.
  • 27
    • 0034371970 scopus 로고    scopus 로고
    • K. Toda, S.-J. Yu, J. Math. Phys. 41 (2000) 4747; K. Toda, S.-J. Yu, J. Nonlinear Math. Phys. Suppl. 8 (2001) 272; K. Toda, S.-J. Yu, Inverse Problems 17 (2001) 1053, and references therein.
    • (2000) J. Math. Phys. , vol.41 , pp. 4747
    • Toda, K.1    Yu, S.-J.2
  • 28
    • 0042403267 scopus 로고    scopus 로고
    • K. Toda, S.-J. Yu, J. Math. Phys. 41 (2000) 4747; K. Toda, S.-J. Yu, J. Nonlinear Math. Phys. Suppl. 8 (2001) 272; K. Toda, S.-J. Yu, Inverse Problems 17 (2001) 1053, and references therein.
    • (2001) J. Nonlinear Math. Phys. Suppl. , vol.8 , pp. 272
    • Toda, K.1    Yu, S.-J.2
  • 29
    • 0035419147 scopus 로고    scopus 로고
    • and references therein
    • K. Toda, S.-J. Yu, J. Math. Phys. 41 (2000) 4747; K. Toda, S.-J. Yu, J. Nonlinear Math. Phys. Suppl. 8 (2001) 272; K. Toda, S.-J. Yu, Inverse Problems 17 (2001) 1053, and references therein.
    • (2001) Inverse Problems , vol.17 , pp. 1053
    • Toda, K.1    Yu, S.-J.2
  • 30
    • 0040587616 scopus 로고
    • O.I. Bogoyavlenskii, Math. USSR-Izv. 34 (1990) 245; F. Calogero, Lett. Nuovo Cimento 14 (1975) 443; J. Schiff, Integrability of Chem-Simons-Higgs vortex equations and a reduction of the selfdual Yang-Mills equations to three dimensions, in: Presented at NATO Adv. Res. Workshop on Painlevé Transcendents, Their Asymptotics and Physical Applications, Ste. Adele, Canada, September 1990, in: NATO ASI B, Vol. 278, Plenum, New York, 1992, p. 393.
    • (1990) Math. USSR-Izv. , vol.34 , pp. 245
    • Bogoyavlenskii, O.I.1
  • 31
    • 51249191266 scopus 로고
    • O.I. Bogoyavlenskii, Math. USSR-Izv. 34 (1990) 245; F. Calogero, Lett. Nuovo Cimento 14 (1975) 443; J. Schiff, Integrability of Chem-Simons-Higgs vortex equations and a reduction of the selfdual Yang-Mills equations to three dimensions, in: Presented at NATO Adv. Res. Workshop on Painlevé Transcendents, Their Asymptotics and Physical Applications, Ste. Adele, Canada, September 1990, in: NATO ASI B, Vol. 278, Plenum, New York, 1992, p. 393.
    • (1975) Lett. Nuovo Cimento , vol.14 , pp. 443
    • Calogero, F.1
  • 32
    • 0011683302 scopus 로고
    • Integrability of Chem-Simons-Higgs vortex equations and a eduction of the selfdual Yang-Mills equations to three dimensions
    • NATO Adv. Res. Workshop on Painlevé Transcendents, Their Asymptotics and Physical Applications, Ste. Adele, Canada, September, Plenum, New York
    • O.I. Bogoyavlenskii, Math. USSR-Izv. 34 (1990) 245; F. Calogero, Lett. Nuovo Cimento 14 (1975) 443; J. Schiff, Integrability of Chem-Simons-Higgs vortex equations and a reduction of the selfdual Yang-Mills equations to three dimensions, in: Presented at NATO Adv. Res. Workshop on Painlevé Transcendents, Their Asymptotics and Physical Applications, Ste. Adele, Canada, September 1990, in: NATO ASI B, Vol. 278, Plenum, New York, 1992, p. 393.
    • (1990) NATO ASI B , vol.278 , pp. 393
    • Schiff, J.1
  • 34
    • 0032545137 scopus 로고    scopus 로고
    • S.-J. Yu, K. Toda, N. Sasa, T. Fukuyama, J. Phys. A 31 (1998) 3337; S.-J. Yu, K. Toda, T. Fukuyama, J. Phys. A 31 (1998) 10181.
    • (1998) J. Phys. A , vol.31 , pp. 10181
    • Yu, S.-J.1    Toda, K.2    Fukuyama, T.3
  • 35
    • 85031077695 scopus 로고    scopus 로고
    • L.D. Paniak, hep-th/0105185
    • L.D. Paniak, hep-th/0105185.
  • 38
    • 18844450034 scopus 로고    scopus 로고
    • Extensions of soliton equations to non-commutative (2 + 1) dimensions
    • Sao Paulo, Brazil, 1-6 July, JHEP PRHEP-unesp2002/038
    • K. Toda, Extensions of soliton equations to non-commutative (2 + 1) dimensions, in: JHEP Proceedings of Workshop on Integrable Theories, Solitons and Duality, Sao Paulo, Brazil, 1-6 July 2002, JHEP PRHEP-unesp2002/038.
    • (2002) JHEP Proceedings of Workshop on Integrable Theories, Solitons and Duality
    • Toda, K.1
  • 39
    • 85031066965 scopus 로고    scopus 로고
    • M. Hamanaka, K. Toda, hep-th/0301213
    • M. Hamanaka, K. Toda, hep-th/0301213.
  • 40
    • 85031067159 scopus 로고    scopus 로고
    • L. Martina, O.K. Pashaev, hep-th/0302055
    • L. Martina, O.K. Pashaev, hep-th/0302055.
  • 42
    • 84980078224 scopus 로고
    • E. Hopf, Commun. Pure Appl. Math. 3 (1950) 201; J.D. Cole, Quart. Appl. Math. 9 (1951) 225.
    • (1951) Quart. Appl. Math. , vol.9 , pp. 225
    • Cole, J.D.1
  • 44
    • 85031068883 scopus 로고    scopus 로고
    • N.A. Nekrasov, hep-th/0010017
    • N.A. Nekrasov, hep-th/0010017.
  • 45
  • 46
    • 0035902084 scopus 로고    scopus 로고
    • hep-th/0012200
    • O. Lechtenfeld, A.D. Popov, B. Spendig, Phys. Lett. B 507 (2001) 317, hep-th/0012200; O. Lechtenfeld, A.D. Popov, B. Spendig, JHEP 0106 (2001) 011, hep-th/0103196.
    • (2001) Phys. Lett. B , vol.507 , pp. 317
    • Lechtenfeld, O.1    Popov, A.D.2    Spendig, B.3
  • 47
    • 0035902084 scopus 로고    scopus 로고
    • hep-th/0103196
    • O. Lechtenfeld, A.D. Popov, B. Spendig, Phys. Lett. B 507 (2001) 317, hep-th/0012200; O. Lechtenfeld, A.D. Popov, B. Spendig, JHEP 0106 (2001) 011, hep-th/0103196.
    • (2001) JHEP , vol.106 , pp. 011
    • Lechtenfeld, O.1    Popov, A.D.2    Spendig, B.3
  • 48
    • 3843049995 scopus 로고    scopus 로고
    • hep-th/0106213
    • O. Lechtenfeld, A.D. Popov, JHEP 0111 (2001) 040, hep-th/0106213; O. Lechtenfeld, A.D. Popov, Phys. Lett. B 523 (2001) 178, hep-th/0108118.
    • (2001) JHEP , vol.111 , pp. 040
    • Lechtenfeld, O.1    Popov, A.D.2
  • 49
    • 0001133114 scopus 로고    scopus 로고
    • hep-th/0108118
    • O. Lechtenfeld, A.D. Popov, JHEP 0111 (2001) 040, hep-th/0106213; O. Lechtenfeld, A.D. Popov, Phys. Lett. B 523 (2001) 178, hep-th/0108118.
    • (2001) Phys. Lett. B , vol.523 , pp. 178
    • Lechtenfeld, O.1    Popov, A.D.2
  • 50
    • 0000235285 scopus 로고
    • H. Ooguri, C. Vafa, Mod. Phys. Lett. A 5 (1990) 1389; H. Ooguri, C. Vafa, Nucl. Phys. B 361 (1991) 469; H. Ooguri, C. Vafa, Nucl. Phys. B 367 (1991) 83.
    • (1990) Mod. Phys. Lett. A , vol.5 , pp. 1389
    • Ooguri, H.1    Vafa, C.2
  • 51
    • 0010136827 scopus 로고
    • H. Ooguri, C. Vafa, Mod. Phys. Lett. A 5 (1990) 1389; H. Ooguri, C. Vafa, Nucl. Phys. B 361 (1991) 469; H. Ooguri, C. Vafa, Nucl. Phys. B 367 (1991) 83.
    • (1991) Nucl. Phys. B , vol.361 , pp. 469
    • Ooguri, H.1    Vafa, C.2
  • 52
    • 13444261191 scopus 로고
    • H. Ooguri, C. Vafa, Mod. Phys. Lett. A 5 (1990) 1389; H. Ooguri, C. Vafa, Nucl. Phys. B 361 (1991) 469; H. Ooguri, C. Vafa, Nucl. Phys. B 367 (1991) 83.
    • (1991) Nucl. Phys. B , vol.367 , pp. 83
    • Ooguri, H.1    Vafa, C.2


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