메뉴 건너뛰기




Volumn 137, Issue 1, 2003, Pages 1396-1405

Geometry of submanifolds derived from spin-valued spectral problems

Author keywords

Clifford algebra; Darboux B cklund transformation; Soliton surfaces; Spin group

Indexed keywords


EID: 0347123020     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026096404956     Document Type: Article
Times cited : (10)

References (35)
  • 1
    • 51249186001 scopus 로고
    • A. Sym, Lett. Nuovo Cimento, 33, 394-400 (1982); 41, 353-360 (1984).
    • (1982) Lett. Nuovo Cimento , vol.33 , pp. 394-400
    • Sym, A.1
  • 2
    • 51249179926 scopus 로고
    • A. Sym, Lett. Nuovo Cimento, 33, 394-400 (1982); 41, 353-360 (1984).
    • (1984) Lett. Nuovo Cimento , vol.41 , pp. 353-360
  • 3
    • 0000315041 scopus 로고
    • Soliton surfaces and their application: Soliton geometry from spectral problems
    • Lect. Notes Phys., Vol. 239, R. Martini, ed., Springer, Berlin
    • A. Sym, "Soliton surfaces and their application: Soliton geometry from spectral problems," in: Geometric Aspects of the Einstein Equations and Integrable Systems (Lect. Notes Phys., Vol. 239, R. Martini, ed.), Springer, Berlin (1985), pp. 154-231.
    • (1985) Geometric Aspects of the Einstein Equations and Integrable Systems , pp. 154-231
    • Sym, A.1
  • 4
    • 0003061298 scopus 로고
    • Surfaces in terms of 2 by 2 matrices: Old and new integrable cases
    • Aspects of Math., Vol. 23, A. P. Fordy and J. C. Wood, eds., Vieweg, Brunswick
    • A. I. Bobenko, "Surfaces in terms of 2 by 2 matrices: Old and new integrable cases," in: Harmonic Maps and Integrable Systems (Aspects of Math., Vol. 23, A. P. Fordy and J. C. Wood, eds.), Vieweg, Brunswick (1994), pp. 83-128; J. Cieśliński, J. Math. Phys., 38, 4255-4272 (1997); "The Darboux-Bianchi-Bäcklund transformations and soliton surfaces," in: Nonlinearity and Geometry (D. Wójcik and J. Cieśliński, eds.), PWN, Warsaw (1998), pp. 81-107; R. K. Dodd, Comm. Math. Phys., 197, 641-665 (1998); A. S. Fokas, I. M. Gelfand, F. Finkel, and Q. M. Liu, Selecta Math., n.s., 6, 347-375 (2000).
    • (1994) Harmonic Maps and Integrable Systems , pp. 83-128
    • Bobenko, A.I.1
  • 5
    • 0039246075 scopus 로고    scopus 로고
    • A. I. Bobenko, "Surfaces in terms of 2 by 2 matrices: Old and new integrable cases," in: Harmonic Maps and Integrable Systems (Aspects of Math., Vol. 23, A. P. Fordy and J. C. Wood, eds.), Vieweg, Brunswick (1994), pp. 83-128; J. Cieśliński, J. Math. Phys., 38, 4255-4272 (1997); "The Darboux-Bianchi-Bäcklund transformations and soliton surfaces," in: Nonlinearity and Geometry (D. Wójcik and J. Cieśliński, eds.), PWN, Warsaw (1998), pp. 81-107; R. K. Dodd, Comm. Math. Phys., 197, 641-665 (1998); A. S. Fokas, I. M. Gelfand, F. Finkel, and Q. M. Liu, Selecta Math., n.s., 6, 347-375 (2000).
    • (1997) J. Math. Phys. , vol.38 , pp. 4255-4272
    • Cieśliński, J.1
  • 6
    • 0038908198 scopus 로고    scopus 로고
    • The Darboux-Bianchi-Bäcklund transformations and soliton surfaces
    • PWN, Warsaw
    • A. I. Bobenko, "Surfaces in terms of 2 by 2 matrices: Old and new integrable cases," in: Harmonic Maps and Integrable Systems (Aspects of Math., Vol. 23, A. P. Fordy and J. C. Wood, eds.), Vieweg, Brunswick (1994), pp. 83-128; J. Cieśliński, J. Math. Phys., 38, 4255-4272 (1997); "The Darboux-Bianchi-Bäcklund transformations and soliton surfaces," in: Nonlinearity and Geometry (D. Wójcik and J. Cieśliński, eds.), PWN, Warsaw (1998), pp. 81-107; R. K. Dodd, Comm. Math. Phys., 197, 641-665 (1998); A. S. Fokas, I. M. Gelfand, F. Finkel, and Q. M. Liu, Selecta Math., n.s., 6, 347-375 (2000).
    • (1998) Nonlinearity and Geometry , pp. 81-107
    • Wójcik, D.1    Cieśliński, J.2
  • 7
    • 0032475783 scopus 로고    scopus 로고
    • A. I. Bobenko, "Surfaces in terms of 2 by 2 matrices: Old and new integrable cases," in: Harmonic Maps and Integrable Systems (Aspects of Math., Vol. 23, A. P. Fordy and J. C. Wood, eds.), Vieweg, Brunswick (1994), pp. 83-128; J. Cieśliński, J. Math. Phys., 38, 4255-4272 (1997); "The Darboux-Bianchi-Bäcklund transformations and soliton surfaces," in: Nonlinearity and Geometry (D. Wójcik and J. Cieśliński, eds.), PWN, Warsaw (1998), pp. 81-107; R. K. Dodd, Comm. Math. Phys., 197, 641-665 (1998); A. S. Fokas, I. M. Gelfand, F. Finkel, and Q. M. Liu, Selecta Math., n.s., 6, 347-375 (2000).
    • (1998) Comm. Math. Phys. , vol.197 , pp. 641-665
    • Dodd, R.K.1
  • 8
    • 0242321048 scopus 로고    scopus 로고
    • n.s.
    • A. I. Bobenko, "Surfaces in terms of 2 by 2 matrices: Old and new integrable cases," in: Harmonic Maps and Integrable Systems (Aspects of Math., Vol. 23, A. P. Fordy and J. C. Wood, eds.), Vieweg, Brunswick (1994), pp. 83-128; J. Cieśliński, J. Math. Phys., 38, 4255-4272 (1997); "The Darboux-Bianchi-Bäcklund transformations and soliton surfaces," in: Nonlinearity and Geometry (D. Wójcik and J. Cieśliński, eds.), PWN, Warsaw (1998), pp. 81-107; R. K. Dodd, Comm. Math. Phys., 197, 641-665 (1998); A. S. Fokas, I. M. Gelfand, F. Finkel, and Q. M. Liu, Selecta Math., n.s., 6, 347-375 (2000).
    • (2000) Selecta Math. , vol.6 , pp. 347-375
    • Fokas, A.S.1    Gelfand, I.M.2    Finkel, F.3    Liu, Q.M.4
  • 12
    • 0000187921 scopus 로고
    • D. Levi and A. Sym, Phys. Lett. A, 149, 381-387 (1990); W. K. Schief, C. Rogers, and M. E. Johnston, Chaos Solitons Fractals, 5, 25-34 (1995); J. Tafel, J. Geom. Phys., 17, 381-390 (1995); D. Korotkin, J. Math. Sci. (New York), 94, 1177-1217 (1999).
    • (1990) Phys. Lett. A , vol.149 , pp. 381-387
    • Levi, D.1    Sym, A.2
  • 13
    • 0002687888 scopus 로고
    • D. Levi and A. Sym, Phys. Lett. A, 149, 381-387 (1990); W. K. Schief, C. Rogers, and M. E. Johnston, Chaos Solitons Fractals, 5, 25-34 (1995); J. Tafel, J. Geom. Phys., 17, 381-390 (1995); D. Korotkin, J. Math. Sci. (New York), 94, 1177-1217 (1999).
    • (1995) Chaos Solitons Fractals , vol.5 , pp. 25-34
    • Schief, W.K.1    Rogers, C.2    Johnston, M.E.3
  • 14
    • 0002046189 scopus 로고
    • D. Levi and A. Sym, Phys. Lett. A, 149, 381-387 (1990); W. K. Schief, C. Rogers, and M. E. Johnston, Chaos Solitons Fractals, 5, 25-34 (1995); J. Tafel, J. Geom. Phys., 17, 381-390 (1995); D. Korotkin, J. Math. Sci. (New York), 94, 1177-1217 (1999).
    • (1995) J. Geom. Phys. , vol.17 , pp. 381-390
    • Tafel, J.1
  • 15
    • 0242380591 scopus 로고    scopus 로고
    • D. Levi and A. Sym, Phys. Lett. A, 149, 381-387 (1990); W. K. Schief, C. Rogers, and M. E. Johnston, Chaos Solitons Fractals, 5, 25-34 (1995); J. Tafel, J. Geom. Phys., 17, 381-390 (1995); D. Korotkin, J. Math. Sci. (New York), 94, 1177-1217 (1999).
    • (1999) J. Math. Sci. (New York) , vol.94 , pp. 1177-1217
    • Korotkin, D.1
  • 18
    • 0000342408 scopus 로고    scopus 로고
    • J. Cieśliński, Adv. Appl. Clifford Algebras, 7, 133-139 (1997); Rend. Sem. Mat. Messina (Proc. Suppl. Messina Conf. 1998), 135-147 (2000).
    • (1997) Adv. Appl. Clifford Algebras , vol.7 , pp. 133-139
    • Cieśliński, J.1
  • 19
    • 0345901074 scopus 로고    scopus 로고
    • Proc. Suppl. Messina Conf. 1998
    • J. Cieśliński, Adv. Appl. Clifford Algebras, 7, 133-139 (1997); Rend. Sem. Mat. Messina (Proc. Suppl. Messina Conf. 1998), 135-147 (2000).
    • (2000) Rend. Sem. Mat. Messina , pp. 135-147
  • 21
    • 0004075836 scopus 로고
    • Nauka, Moscow
    • V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaievsky, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transi.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); V. E. Zakharov and A. V. Mikhailov, Comm. Math. Phys., 74, 21-40 (1980); V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin (1991); R. Meinel, G. Neugebauer, and H. Steudel, Solitonen: Nichtlineare Strukturen, Academie; Berlin (1991); C.-H. Gu, "Bäcklund transformations and Darboux transformations, " in: Soliton Theory and Its Applications (C.-H. Gu, ed.), Springer, Berlin (1995), pp. 122-151; J. Cieśliński, J. Math. Phys., 36, 5670-5706 (1995).
    • (1980) Theory of Solitons: The Inverse Scattering Method [in Russian]
    • Zakharov, V.E.1    Manakov, S.V.2    Novikov, S.P.3    Pitaievsky, L.P.4
  • 22
    • 0346532048 scopus 로고    scopus 로고
    • English transl., Plenum, New York (1984)
    • V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaievsky, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transi.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); V. E. Zakharov and A. V. Mikhailov, Comm. Math. Phys., 74, 21-40 (1980); V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin (1991); R. Meinel, G. Neugebauer, and H. Steudel, Solitonen: Nichtlineare Strukturen, Academie; Berlin (1991); C.-H. Gu, "Bäcklund transformations and Darboux transformations, " in: Soliton Theory and Its Applications (C.-H. Gu, ed.), Springer, Berlin (1995), pp. 122-151; J. Cieśliński, J. Math. Phys., 36, 5670-5706 (1995).
    • Novikov, S.P.1    Manakov, S.V.2    Pitaevsky, L.P.3    Zakharov, V.E.4
  • 23
    • 0040340516 scopus 로고
    • V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaievsky, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transi.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); V. E. Zakharov and A. V. Mikhailov, Comm. Math. Phys., 74, 21-40 (1980); V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin (1991); R. Meinel, G. Neugebauer, and H. Steudel, Solitonen: Nichtlineare Strukturen, Academie; Berlin (1991); C.-H. Gu, "Bäcklund transformations and Darboux transformations, " in: Soliton Theory and Its Applications (C.-H. Gu, ed.), Springer, Berlin (1995), pp. 122-151; J. Cieśliński, J. Math. Phys., 36, 5670-5706 (1995).
    • (1980) Comm. Math. Phys. , vol.74 , pp. 21-40
    • Zakharov, V.E.1    Mikhailov, A.V.2
  • 24
    • 0004025430 scopus 로고
    • Springer, Berlin
    • V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaievsky, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transi.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); V. E. Zakharov and A. V. Mikhailov, Comm. Math. Phys., 74, 21-40 (1980); V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin (1991); R. Meinel, G. Neugebauer, and H. Steudel, Solitonen: Nichtlineare Strukturen, Academie; Berlin (1991); C.-H. Gu, "Bäcklund transformations and Darboux transformations, " in: Soliton Theory and Its Applications (C.-H. Gu, ed.), Springer, Berlin (1995), pp. 122-151; J. Cieśliński, J. Math. Phys., 36, 5670-5706 (1995).
    • (1991) Darboux Transformations and Solitons
    • Matveev, V.B.1    Salle, M.A.2
  • 25
    • 0040773400 scopus 로고
    • Academie; Berlin
    • V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaievsky, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transi.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); V. E. Zakharov and A. V. Mikhailov, Comm. Math. Phys., 74, 21-40 (1980); V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin (1991); R. Meinel, G. Neugebauer, and H. Steudel, Solitonen: Nichtlineare Strukturen, Academie; Berlin (1991); C.-H. Gu, "Bäcklund transformations and Darboux transformations, " in: Soliton Theory and Its Applications (C.-H. Gu, ed.), Springer, Berlin (1995), pp. 122-151; J. Cieśliński, J. Math. Phys., 36, 5670-5706 (1995).
    • (1991) Solitonen: Nichtlineare Strukturen
    • Meinel, R.1    Neugebauer, G.2    Steudel, H.3
  • 26
    • 0346803331 scopus 로고
    • Bäcklund transformations and Darboux transformations
    • C.-H. Gu, ed., Springer, Berlin
    • V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaievsky, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transi.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); V. E. Zakharov and A. V. Mikhailov, Comm. Math. Phys., 74, 21-40 (1980); V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin (1991); R. Meinel, G. Neugebauer, and H. Steudel, Solitonen: Nichtlineare Strukturen, Academie; Berlin (1991); C.-H. Gu, "Bäcklund transformations and Darboux transformations, " in: Soliton Theory and Its Applications (C.-H. Gu, ed.), Springer, Berlin (1995), pp. 122-151; J. Cieśliński, J. Math. Phys., 36, 5670-5706 (1995).
    • (1995) Soliton Theory and Its Applications , pp. 122-151
    • Gu, C.-H.1
  • 27
    • 21844502946 scopus 로고
    • V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaievsky, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transi.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); V. E. Zakharov and A. V. Mikhailov, Comm. Math. Phys., 74, 21-40 (1980); V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer, Berlin (1991); R. Meinel, G. Neugebauer, and H. Steudel, Solitonen: Nichtlineare Strukturen, Academie; Berlin (1991); C.-H. Gu, "Bäcklund transformations and Darboux transformations, " in: Soliton Theory and Its Applications (C.-H. Gu, ed.), Springer, Berlin (1995), pp. 122-151; J. Cieśliński, J. Math. Phys., 36, 5670-5706 (1995).
    • (1995) J. Math. Phys. , vol.36 , pp. 5670-5706
    • Cieśliński, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.