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Volumn 15, Issue 6, 2003, Pages 559-628

On the moduli of a quantized elastica in P and KdV flows: Study of hyperelliptic curves as an extension of Euler's perspective of elastica I

Author keywords

Elastica; Hyperelliptic function; Loop space; Polymer; Statistical mechanics

Indexed keywords


EID: 0141705194     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X03001722     Document Type: Article
Times cited : (14)

References (61)
  • 1
    • 84968511025 scopus 로고
    • The influence of elasticity on analysis: The classic heritage
    • C. Truesdell, The influence of elasticity on analysis: The classic heritage, Bull. Amer. Math. Soc. 9 (1983), 293-310.
    • (1983) Bull. Amer. Math. Soc. , vol.9 , pp. 293-310
    • Truesdell, C.1
  • 6
    • 0002651956 scopus 로고
    • Elastica and computer vision
    • ed. C. Bajaj, Springer-Verlag, Berlin
    • D. Mumford, "Elastica and computer vision" in Algebraic Geometry and its Applications, ed. C. Bajaj, Springer-Verlag, Berlin, 1993, pp. 507-518.
    • (1993) Algebraic Geometry and its Applications , pp. 507-518
    • Mumford, D.1
  • 9
    • 0002846809 scopus 로고
    • Poisson geometry of the filament equation
    • J. Langer and R. Perline, Poisson geometry of the filament equation, J. Nonlinear Sci. 1 (1991), 71-91.
    • (1991) J. Nonlinear Sci. , vol.1 , pp. 71-91
    • Langer, J.1    Perline, R.2
  • 11
    • 51249179487 scopus 로고
    • Loop groups and equations of KdV type
    • G. Segal and G. Wilson, Loop groups and equations of KdV type, IHES 61 (1985), 5-65.
    • (1985) IHES , vol.61 , pp. 5-65
    • Segal, G.1    Wilson, G.2
  • 12
    • 0000343451 scopus 로고
    • Geometrical construction of the Hirota bilinear form of the modified Korteweg-de Vries equation on a thin elastic rod: Bosonic classical theory
    • S. Matsutani, Geometrical construction of the Hirota bilinear form of the modified Korteweg-de Vries equation on a thin elastic rod: Bosonic classical theory, Int. J. Mod. Phys. A 22 (1995), 3109-3123.
    • (1995) Int. J. Mod. Phys. A , vol.22 , pp. 3109-3123
    • Matsutani, S.1
  • 13
    • 0032549423 scopus 로고    scopus 로고
    • Statistical mechanics of elastica on plane: Origin of MKdV hierarchy
    • S. Matsutani, Statistical mechanics of elastica on plane: origin of MKdV hierarchy, J. Phys. A 31 (1998), 2705-2725.
    • (1998) J. Phys. A , vol.31 , pp. 2705-2725
    • Matsutani, S.1
  • 15
    • 0000286629 scopus 로고    scopus 로고
    • Some geometrical and topological problems in polymer physics
    • A. L. Kholodenko and T. A. Vilgis, Some geometrical and topological problems in polymer physics, Phys. Rep. 298 (1998), 251-370.
    • (1998) Phys. Rep. , vol.298 , pp. 251-370
    • Kholodenko, A.L.1    Vilgis, T.A.2
  • 16
    • 0141783057 scopus 로고    scopus 로고
    • a talk at the Meeting on "Study on Integrability in Differential Geometry", Lecture on Tokyo Metropritan University, Jan. 8-10
    • F. Pedit, KdV flows on the Riemann sphere, a talk at the meeting on "Study on Integrability in Differential Geometry", Lecture on Tokyo Metropritan University, Jan. 8-10, 1998.
    • (1998) KdV Flows on the Riemann Sphere
    • Pedit, F.1
  • 17
    • 0009888442 scopus 로고    scopus 로고
    • Closed loop solitons and sigma functions: Classical and quantized elasticas with Genera one and two
    • S. Matsutani, Closed loop solitons and sigma functions: Classical and quantized elasticas with Genera one and two, J. Geom. Phys. 39 (2001), 50-61.
    • (2001) J. Geom. Phys. , vol.39 , pp. 50-61
    • Matsutani, S.1
  • 18
    • 0035827486 scopus 로고    scopus 로고
    • Hyperelliptic solutions of KdV and KP equations: Reevaluation of Baker's study on hyperelliptic sigma functions
    • S. Matsutani, Hyperelliptic solutions of KdV and KP equations: Reevaluation of Baker's study on hyperelliptic sigma functions, J. Phys. A 34 (2001), 4721-4732.
    • (2001) J. Phys. A , vol.34 , pp. 4721-4732
    • Matsutani, S.1
  • 19
    • 0036331647 scopus 로고    scopus 로고
    • Hyperelliptic loop solitons with Genus g: Investigations of a quantized elastica
    • S. Matsutani, Hyperelliptic loop solitons with Genus g: Investigations of a quantized elastica, J. Geom. Phys. 43 (2002), 146-162.
    • (2002) J. Geom. Phys. , vol.43 , pp. 146-162
    • Matsutani, S.1
  • 20
    • 0037123905 scopus 로고    scopus 로고
    • Explicit hyperelliptic solutions of modified Korteweg-de Vries equation: Essentials of Miura transformation
    • S. Matsutani, Explicit hyperelliptic solutions of modified Korteweg-de Vries equation: Essentials of Miura transformation, J. Phys. A. Math & Gen. 35 (2002), 4321-4333.
    • (2002) J. Phys. A. Math & Gen. , vol.35 , pp. 4321-4333
    • Matsutani, S.1
  • 21
    • 84973997896 scopus 로고
    • Orientation and string structures on loop spaces
    • C. MacLaughlin, Orientation and string structures on loop spaces, Pac. J. Math 155:1 (1992), 143-156.
    • (1992) Pac. J. Math , vol.155 , Issue.1 , pp. 143-156
    • MacLaughlin, C.1
  • 23
    • 0141448156 scopus 로고
    • D-Modules and nonlinear system
    • M. Sato, D-Modules and nonlinear system, Adv. Stud. Pure Math. 19 (1989), 417-434.
    • (1989) Adv. Stud. Pure Math. , vol.19 , pp. 417-434
    • Sato, M.1
  • 25
    • 0010043257 scopus 로고
    • Nonlinear partial differentail equations in applied science
    • eds. H. Fujita, P. D. Lax and G. Strang, Kinokuniya/North-Holland, Tokyo
    • M. Sato and Y. Sato, Soliton equations as dynamical systems on infinite dimensional Grassmann manifold, Nonlinear Partial Differentail Equations in Applied Science, eds. H. Fujita, P. D. Lax and G. Strang, Kinokuniya/North-Holland, Tokyo, 1983.
    • (1983) Soliton Equations as Dynamical Systems on Infinite Dimensional Grassmann Manifold
    • Sato, M.1    Sato, Y.2
  • 26
    • 84972510505 scopus 로고
    • Cohomological structure in soliton equations and Jacobian varieties
    • M. Mulase, Cohomological structure in soliton equations and Jacobian varieties, J. Diff. Geom. (1984), 403-430.
    • (1984) J. Diff. Geom. , pp. 403-430
    • Mulase, M.1
  • 27
    • 0010989303 scopus 로고
    • Methods of algebraic geomtery in the theory of nonlinear equations
    • I. M. Krichever, Methods of algebraic geomtery in the theory of nonlinear equations, Russian Math. Surverys 32 (1977), 185-213.
    • (1977) Russian Math. Surverys , vol.32 , pp. 185-213
    • Krichever, I.M.1
  • 29
    • 0000252859 scopus 로고
    • On a system of differential equations leading to periodic functions
    • H. F. Baker, On a system of differential equations leading to periodic functions, Acta Math. 27 (1903), 135-156.
    • (1903) Acta Math. , vol.27 , pp. 135-156
    • Baker, H.F.1
  • 33
    • 0034420622 scopus 로고    scopus 로고
    • 4: Further generalized Weierstrass relation
    • 4: Further generalized Weierstrass relation, Rev. Math. Phys. 12 (2000), 431-444.
    • (2000) Rev. Math. Phys. , vol.12 , pp. 431-444
    • Matsutani, S.1
  • 35
    • 0004261486 scopus 로고
    • Papers on Fuchsian functions
    • Springer
    • H. Poincaré, Papers on Fuchsian functions, J. Stillwel, Springer, 1985.
    • (1985) J. Stillwel
    • Poincaré, H.1
  • 36
    • 0009146101 scopus 로고
    • Cambridge University Press, Cambridge
    • H. F. Baker, Abelian Functions, Cambridge University Press, Cambridge, 1897.
    • (1897) Abelian Functions
    • Baker, H.F.1
  • 37
    • 0001678450 scopus 로고
    • The Korteweg-de Vries hierarchy as dynamics of closed curves in the plane
    • R. E. Goldstein and D. M. Petrich, The Korteweg-de Vries hierarchy as dynamics of closed curves in the plane, Phys. Rev. Lett. 67 (1991), 3203-3206.
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 3203-3206
    • Goldstein, R.E.1    Petrich, D.M.2
  • 38
    • 4243894773 scopus 로고
    • Solitons, Euler's equation, and vortex patch dynamics
    • R. E. Goldstein and D. M. Petrich, Solitons, Euler's equation, and vortex patch dynamics, Phys. Rev. Lett. 67 (1992), 555-558.
    • (1992) Phys. Rev. Lett. , vol.67 , pp. 555-558
    • Goldstein, R.E.1    Petrich, D.M.2
  • 43
    • 0010071611 scopus 로고
    • Commutative ordinary differential operators
    • by J. L. Burchnall and T. W. Chaundy
    • H. F. Baker, Note the foregoing paper "Commutative Ordinary Differential Operators" by J. L. Burchnall and T. W. Chaundy, Proc. Royal Society London (A) 118 (1928), 584-593.
    • (1928) Proc. Royal Society London (A) , vol.118 , pp. 584-593
    • Baker, H.F.1
  • 44
    • 0000885783 scopus 로고
    • An algebro-geometric construction of commuting operators and of solutions to the Toda latticd equation, Korteweg-de Vries equation and related non-linear equation
    • Kyoto
    • D. Mumford, An algebro-geometric construction of commuting operators and of solutions to the Toda latticd equation, Korteweg-de Vries equation and related non-linear equation, Intl. Symp. on Algebraic Geomtery (1977), Kyoto, 115-153.
    • (1977) Intl. Symp. on Algebraic Geomtery , pp. 115-153
    • Mumford, D.1
  • 45
    • 77956456169 scopus 로고
    • Analytic extensions of differentiable functions defined in closed sets
    • H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89.
    • (1934) Trans. Amer. Math. Soc. , vol.36 , pp. 63-89
    • Whitney, H.1
  • 48
    • 0040686988 scopus 로고
    • The physical realization of the Jimbo-Miwa theory of the modified Korteweg-de Vries equation on a thin elastic rod: Fermionic theory
    • S. Matsutani, The physical realization of the Jimbo-Miwa theory of the modified Korteweg-de Vries equation on a thin elastic rod: Fermionic theory, Int. J. Mod. Phys. A 10 (1995), 3091-3107.
    • (1995) Int. J. Mod. Phys. A , vol.10 , pp. 3091-3107
    • Matsutani, S.1
  • 49
  • 56
    • 84968502650 scopus 로고
    • Modulus space is simply-connected
    • C. Maclachlan, Modulus space is simply-connected, Proc. A.M.S. 29 (1971), 85-86.
    • (1971) Proc. A.M.S. , vol.29 , pp. 85-86
    • Maclachlan, C.1
  • 59
    • 24444461010 scopus 로고
    • Ghosts and geometry
    • J. M. Leinass and K. Olaussen, Ghosts and geometry, Phys. Lett. 108B (1982), 199-202.
    • (1982) Phys. Lett. , vol.108 B , pp. 199202
    • Leinass, J.M.1    Olaussen, K.2
  • 61
    • 0002106116 scopus 로고    scopus 로고
    • Induced surfaces and their integrable dynamics
    • B. G. Knopelchenko, Induced surfaces and their integrable dynamics, Studies in Appl. Math. 98 (1996), 9-51.
    • (1996) Studies in Appl. Math. , vol.98 , pp. 9-51
    • Knopelchenko, B.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.