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Volumn 38, Issue 8, 1997, Pages 4255-4272

A generalized formula for integrable classes of surfaces in Lie algebras

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EID: 0039246075     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532093     Document Type: Article
Times cited : (39)

References (48)
  • 1
    • 0012849869 scopus 로고
    • Bäcklund transformations at the turn of the century
    • edited by R. M. Miura Springer-Verlag, Berlin
    • G. L. Lamb, Jr., "Bäcklund transformations at the turn of the century," in Bäcklund transformations, edited by R. M. Miura (Springer-Verlag, Berlin, 1976), pp. 69-79.
    • (1976) Bäcklund Transformations , pp. 69-79
    • Lamb G.L., Jr.1
  • 3
    • 0000315041 scopus 로고
    • Soliton surfaces and their applications
    • Geometric Aspects of the Einstein Equations and Integrable Systems, edited by R. Martini (Springer-Verlag, Berlin)
    • A. Sym, "Soliton surfaces and their applications," in Geometric Aspects of the Einstein Equations and Integrable Systems, edited by R. Martini (Lecture Notes in Physics No. 239), (Springer-Verlag, Berlin, 1985), pp. 154-231.
    • (1985) Lecture Notes in Physics , vol.239 , pp. 154-231
    • Sym, A.1
  • 4
    • 0347668804 scopus 로고
    • 3 as an example of soliton surfaces
    • Proceedings of the 7th NEEDS conference, Baia Verde, Gallipoli, Italy, June 1991, edited by M. Boiti, L. Martina, and L. Pempinelli World Scientific, Singapore
    • 3 as an example of soliton surfaces," in Nonlinear Evolution Equations and Dynamical Systems, Proceedings of the 7th NEEDS conference, Baia Verde, Gallipoli, Italy, June 1991, edited by M. Boiti, L. Martina, and L. Pempinelli (World Scientific, Singapore, 1992), pp. 111-117.
    • (1992) Nonlinear Evolution Equations and Dynamical Systems , pp. 111-117
    • Doliwa, A.A.1    Sym, A.2
  • 5
    • 0003061298 scopus 로고
    • Surfaces in Terms of 2 by 2 Matrices. Old and New Integrable Cases
    • Harmonic maps and integrable systems edited by A. P. Fordy and J. C. Wood 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 Mathematics, vol. 23), edited by A. P. Fordy and J. C. Wood (Vieweg, Brunswick, 1994).
    • (1994) Aspects of Mathematics , vol.23
    • Bobenko, A.I.1
  • 8
    • 0001911367 scopus 로고
    • Lie symmetries as a tool to isolate integrable geometries
    • Proceedings of the 7th NEEDS conference, Baia Verde, Gallipoli, Italy, June 1991, edited by M. Boiti, L. Martina, and L. Pempinelli World Scientific, Singapore
    • J. Cieśliński, "Lie symmetries as a tool to isolate integrable geometries," in Nonlinear Evolution Equations and Dynamical Systems, Proceedings of the 7th NEEDS conference, Baia Verde, Gallipoli, Italy, June 1991, edited by M. Boiti, L. Martina, and L. Pempinelli (World Scientific, Singapore, 1992), pp. 260-268.
    • (1992) Nonlinear Evolution Equations and Dynamical Systems , pp. 260-268
    • Cieśliński, J.1
  • 9
    • 0002439927 scopus 로고
    • Integration of nonlinear equations of mathematical physics by the inverse scattering method II
    • in Russian
    • V. E. Zakharov and A. B. Shabat, "Integration of nonlinear equations of mathematical physics by the inverse scattering method II," Funk. Anal. Pril. 13, 13-22 (1979) (in Russian).
    • (1979) Funk. Anal. Pril. , vol.13 , pp. 13-22
    • Zakharov, V.E.1    Shabat, A.B.2
  • 10
    • 51249186001 scopus 로고
    • Soliton Surfaces
    • A. Sym, "Soliton Surfaces," Lett. Nuovo Cimen. 33, 394-400 (1982).
    • (1982) Lett. Nuovo Cimen. , vol.33 , pp. 394-400
    • Sym, A.1
  • 11
    • 51249182914 scopus 로고
    • Soliton Surfaces II. Geometric Unification of Solvable Nonlinearities
    • A. Sym, "Soliton Surfaces II. Geometric Unification of Solvable Nonlinearities," Lett. Nuovo Cimen. 36, 307-312 (1983).
    • (1983) Lett. Nuovo Cimen. , vol.36 , pp. 307-312
    • Sym, A.1
  • 12
    • 0000187921 scopus 로고
    • Integrable systems describing surfaces of non-constant curvature
    • D. Levi and A. Sym, "Integrable systems describing surfaces of non-constant curvature," Phys. Lett. A 149, 381-387 (1990).
    • (1990) Phys. Lett. A , vol.149 , pp. 381-387
    • Levi, D.1    Sym, A.2
  • 14
    • 51249182230 scopus 로고
    • Soliton Surfaces III. Solvable nonlinearities with trivial geometry
    • A. Sym, "Soliton Surfaces III. Solvable nonlinearities with trivial geometry," Lett. Nuovo Cimen. 39, 193-196 (1984).
    • (1984) Lett. Nuovo Cimen. , vol.39 , pp. 193-196
    • Sym, A.1
  • 15
    • 51249185668 scopus 로고
    • Soliton Surfaces IV. Topological Charge for 'Nontopological' Solitons
    • A. Sym, "Soliton Surfaces IV. Topological Charge for 'Nontopological' Solitons," Lett. Nuovo Cimen. 40, 225-231 (1984).
    • (1984) Lett. Nuovo Cimen. , vol.40 , pp. 225-231
    • Sym, A.1
  • 16
    • 51249186457 scopus 로고
    • Soliton Surfaces V. Geometric Theory of Loop Solitons
    • A. Sym, "Soliton Surfaces V. Geometric Theory of Loop Solitons," Lett. Nuovo Cimen. 41, 33-40 (1984).
    • (1984) Lett. Nuovo Cimen. , vol.41 , pp. 33-40
    • Sym, A.1
  • 17
    • 51249179926 scopus 로고
    • Soliton Surfaces VI. Gauge Invariance and Final Formulation of the Approach
    • A. Sym, "Soliton Surfaces VI. Gauge Invariance and Final Formulation of the Approach," Lett. Nuovo Cimen. 41, 353-360 (1984).
    • (1984) Lett. Nuovo Cimen. , vol.41 , pp. 353-360
    • Sym, A.1
  • 18
    • 77951503382 scopus 로고
    • Soliton Surfaces VII. Relativistic String in External Field: General Integral and Particular Solutions
    • A. Sym, O. Ragnisco, D. Levi, and M. Bruschi, "Soliton Surfaces VII. Relativistic String in External Field: General Integral and Particular Solutions," Lett. Nuovo Cimen. 44, 529-536 (1985).
    • (1985) Lett. Nuovo Cimen. , vol.44 , pp. 529-536
    • Sym, A.1    Ragnisco, O.2    Levi, D.3    Bruschi, M.4
  • 19
    • 51149213194 scopus 로고
    • Exact Solution to Localized-Induction-Approximation Equation Modelling Smoke Ring Motion
    • J. Cieśliński, P. K. H. Gragert, and A. Sym, "Exact Solution to Localized-Induction-Approximation Equation Modelling Smoke Ring Motion," Phys. Rev. Lett. 57, 1507-1510 (1986).
    • (1986) Phys. Rev. Lett. , vol.57 , pp. 1507-1510
    • Cieśliński, J.1    Gragert, P.K.H.2    Sym, A.3
  • 20
    • 18144378995 scopus 로고
    • An effective method to compute N-soliton Darboux matrix and N-soliton surfaces
    • J. Cieśliński, "An effective method to compute N-soliton Darboux matrix and N-soliton surfaces," J. Math. Phys. 32, 2395-2399 (1991).
    • (1991) J. Math. Phys. , vol.32 , pp. 2395-2399
    • Cieśliński, J.1
  • 21
    • 0026021651 scopus 로고
    • Three-dimensional distortions of a vortex filament with axial flow
    • Y. Fukumoto and T. Miyazaki, "Three-dimensional distortions of a vortex filament with axial flow," J. Fluid Mech. 222, 369-416 (1991).
    • (1991) J. Fluid Mech. , vol.222 , pp. 369-416
    • Fukumoto, Y.1    Miyazaki, T.2
  • 23
    • 0000409772 scopus 로고
    • 3 in terms of theta functions
    • 3 in terms of theta functions," Math. Ann. 290, 209-245 (1991).
    • (1991) Math. Ann. , vol.290 , pp. 209-245
    • Bobenko, A.I.1
  • 25
    • 0002046189 scopus 로고
    • 3 with prescribed curvature
    • 3 with prescribed curvature," J. Geom. Phys. 17, 381-390 (1995).
    • (1995) J. Geom. Phys. , vol.17 , pp. 381-390
    • Tafel, J.1
  • 26
    • 85033158175 scopus 로고    scopus 로고
    • Discrete Surfaces with constant Negative Gaussian Curvature and the Hirota Equation
    • to be published
    • A. Bobenko and U. Pinkall: "Discrete Surfaces with constant Negative Gaussian Curvature and the Hirota Equation," to be published in J. Diff. Geom.
    • J. Diff. Geom.
    • Bobenko, A.1    Pinkall, U.2
  • 27
    • 25144479070 scopus 로고    scopus 로고
    • Discrete Isothermic Surfaces
    • A. Bobenko and U. Pinkall, "Discrete Isothermic Surfaces," J. Reine Angew Math. 475, 187-208 (1996).
    • (1996) J. Reine Angew Math. , vol.475 , pp. 187-208
    • Bobenko, A.1    Pinkall, U.2
  • 28
    • 0030529761 scopus 로고    scopus 로고
    • Surfaces on Lie groups, on Lie algebras and Their Integrability
    • A. S. Fokas and I. M. Gelfand, "Surfaces on Lie groups, on Lie algebras and Their Integrability," Commu. Math. Phys. 177, 203-220 (1996).
    • (1996) Commu. Math. Phys. , vol.177 , pp. 203-220
    • Fokas, A.S.1    Gelfand, I.M.2
  • 29
    • 0000373514 scopus 로고
    • Surfaces in Minkowski 3-space on which H and K are linearly related
    • T. K. Milnor, "Surfaces in Minkowski 3-space on which H and K are linearly related," Mich. Math. J. 30, 309-315 (1983).
    • (1983) Mich. Math. J. , vol.30 , pp. 309-315
    • Milnor, T.K.1
  • 30
    • 0002074636 scopus 로고
    • Weingarten Surfaces and Nonlinear Partial Differential Equations
    • H. Wu. "Weingarten Surfaces and Nonlinear Partial Differential Equations," Ann. Glob. Anal. Geom. 11, 49-64 (1993).
    • (1993) Ann. Glob. Anal. Geom. , vol.11 , pp. 49-64
    • Wu, H.1
  • 36
  • 37
    • 21844502946 scopus 로고
    • An algebraic method to construct the Darboux matrix
    • J. Cieśliński, "An algebraic method to construct the Darboux matrix," J. Math. Phys. 36, 5670-5706 (1995).
    • (1995) J. Math. Phys. , vol.36 , pp. 5670-5706
    • Cieśliński, J.1
  • 38
    • 21844515508 scopus 로고
    • Bäcklund transformations of linear Weingarten surfaces in Minkowski three-space
    • S. G. Buyske, "Bäcklund transformations of linear Weingarten surfaces in Minkowski three-space," J. Math. Phys. 35, 4719-4724 (1994).
    • (1994) J. Math. Phys. , vol.35 , pp. 4719-4724
    • Buyske, S.G.1
  • 39
    • 0010898989 scopus 로고
    • typescript
    • 2," typescript, 1995.
    • (1995) 2
    • Tian, C.1
  • 41
    • 0346141747 scopus 로고
    • Classically Solvable Field Theory Model
    • F. Lund, "Classically Solvable Field Theory Model," Ann. Phys. 115, 251-268 (1978).
    • (1978) Ann. Phys. , vol.115 , pp. 251-268
    • Lund, F.1
  • 42
    • 0001719572 scopus 로고
    • Soliton equations and pseudospherical surfaces
    • R. Sasaki, "Soliton equations and pseudospherical surfaces," Nucl. Phys. B 154, 343-357 (1979).
    • (1979) Nucl. Phys. B , vol.154 , pp. 343-357
    • Sasaki, R.1
  • 43
    • 0007245253 scopus 로고
    • Nonlocal trends in the Geometry of Differential Equations: Symmetries, Conservation Laws, and Bäcklund Transformations
    • I. V. Krasil'shchik and A. M. Vinogradov, "Nonlocal trends in the Geometry of Differential Equations: Symmetries, Conservation Laws, and Bäcklund Transformations," Acta Appl. Math. 15, 161-209 (1989).
    • (1989) Acta Appl. Math. , vol.15 , pp. 161-209
    • Krasil'shchik, I.V.1    Vinogradov, A.M.2
  • 45
    • 21344496135 scopus 로고
    • On integrability of the inhomogeneous Heisenberg ferromagnet model: Examination of a new test
    • J. Cieśliński, P. Goldstein, and A. Sym, "On integrability of the inhomogeneous Heisenberg ferromagnet model: examination of a new test," J. Phys. A: Math. Gen. 27, 1645-1664 (1994).
    • (1994) J. Phys. A: Math. Gen. , vol.27 , pp. 1645-1664
    • Cieśliński, J.1    Goldstein, P.2    Sym, A.3
  • 46
    • 21144473275 scopus 로고
    • Group interpretation of the spectral parameter in the case of the Nonhomogeneous, Nonlinear Schrödinger System
    • J. Cieśliński, "Group interpretation of the spectral parameter in the case of the Nonhomogeneous, Nonlinear Schrödinger System," J. Math. Phys. 34, 2372-2384 (1993).
    • (1993) J. Math. Phys. , vol.34 , pp. 2372-2384
    • Cieśliński, J.1
  • 47
    • 0000287170 scopus 로고
    • An elementary geometric characterization of the integrable motions of a curve
    • A. Doliwa and P. Santini, "An elementary geometric characterization of the integrable motions of a curve," Phys. Lett. A 185, 373-384 (1994).
    • (1994) Phys. Lett. A , vol.185 , pp. 373-384
    • Doliwa, A.1    Santini, P.2
  • 48
    • 0002269987 scopus 로고    scopus 로고
    • The integrable dynamics of a discrete curve
    • Symmetries and Integrability of Difference Equations, edited by D. Levi, L. Vinet, and P. Winternitz, American Mathematical Society, Providence
    • A. Doliwa and P. Santini, "The integrable dynamics of a discrete curve," in Symmetries and Integrability of Difference Equations, edited by D. Levi, L. Vinet, and P. Winternitz, CRM Proceedings & Lecture Notes, Vol. 9 (American Mathematical Society, Providence, 1996), pp. 91-102.
    • (1996) CRM Proceedings & Lecture Notes , vol.9 , pp. 91-102
    • Doliwa, A.1    Santini, P.2


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