메뉴 건너뛰기




Volumn 221, Issue 1, 2001, Pages 197-227

The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035641135     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005573     Document Type: Article
Times cited : (90)

References (69)
  • 1
    • 0039347964 scopus 로고    scopus 로고
    • On the weak Kowalevski-Painlevé property for hyperelliptically separable systems
    • Abenda, S., Fedorov, Yu. [2000]: On the weak Kowalevski-Painlevé property for hyperelliptically separable systems. Acta Appl. Math. 60 (2), 137-178
    • (2000) Acta Appl. Math. , vol.60 , Issue.2 , pp. 137-178
    • Abenda, S.1    Fedorov, Yu.2
  • 3
    • 0000998563 scopus 로고
    • Investigation of equations of Korteweg de Vries type by the method of recurrence relations
    • Alber, S.J. [1979]: Investigation of equations of Korteweg de Vries type by the method of recurrence relations. (Russian) J. Lond. Math. Soc. (2) 19, no. 3, 467-480
    • (1979) (Russian) J. Lond. Math. Soc. (2) , vol.19 , Issue.3 , pp. 467-480
    • Alber, S.J.1
  • 4
    • 0002167082 scopus 로고
    • Hamiltonian formalism for finite-zone solutions of integrable equations
    • Alber, M.S., Alber, S.J. [1985]: Hamiltonian formalism for finite-zone solutions of integrable equations. C. R. Acad. Sci. Paris Ser. I Math. 301, 777-781
    • (1985) C. R. Acad. Sci. Paris Ser. I Math. , vol.301 , pp. 777-781
    • Alber, M.S.1    Alber, S.J.2
  • 5
    • 0000310316 scopus 로고
    • The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
    • Alber, M.S., Camassa, R., Holm, D.D. and Marsden, J.E. [1994]: The geometry of peaked solitons and billiard solutions of a class of integrable PDE's. Lett. Math. Phys. 32, 137-151
    • (1994) Lett. Math. Phys. , vol.32 , pp. 137-151
    • Alber, M.S.1    Camassa, R.2    Holm, D.D.3    Marsden, J.E.4
  • 6
    • 0000960226 scopus 로고
    • On the link between umbilic geodesics and soliton solutions of nonlinear PDE's
    • Alber, M.S., Camassa, R., Holm, D.D. and Marsden, J.E. [1995]: On the link between umbilic geodesics and soliton solutions of nonlinear PDE's. Proc. Roy. Soc. 450, 677-692
    • (1995) Proc. Roy. Soc. , vol.450 , pp. 677-692
    • Alber, M.S.1    Camassa, R.2    Holm, D.D.3    Marsden, J.E.4
  • 8
    • 0038019338 scopus 로고    scopus 로고
    • On peak on solutions of the shallow water equation
    • Alber, M.S. and Miller, C. [2001]: On peak on solutions of the shallow water equation. Appl. Math. Lett. 14, 93-98
    • (2001) Appl. Math. Lett. , vol.14 , pp. 93-98
    • Alber, M.S.1    Miller, C.2
  • 9
    • 0034367365 scopus 로고    scopus 로고
    • Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
    • Alber, M.S. and Fedorov, Yu.N. [2000]: Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians. J. Phys. A: Math. Gen. 33, 8409-8425
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 8409-8425
    • Alber, M.S.1    Fedorov, Yu.N.2
  • 10
    • 0035420587 scopus 로고    scopus 로고
    • Algebraic geometric solutions for nonlinear evolution equations and flows on the nonlinear subvarieties of Jacobians
    • to appear
    • Alber, M.S. and Fedorov, Yu.N. [2001]: Algebraic geometric solutions for nonlinear evolution equations and flows on the nonlinear subvarieties of Jacobians. Inverse Problems (to appear)
    • (2001) Inverse Problems
    • Alber, M.S.1    Fedorov, Yu.N.2
  • 11
    • 0010969089 scopus 로고    scopus 로고
    • Complex billiard Hamiltonian systems and nonlinear waves
    • Fokas, Y.H., Gelfand, I. M. (eds.) Algebraic Aspects of Integrable Systems. Boston: Birkhäuser
    • Alber, M.S., Luther, G.G., and Marsden, J.E. [1997]: Complex billiard Hamiltonian systems and nonlinear waves. In: Fokas, Y.H., Gelfand, I. M. (eds.) Algebraic Aspects of Integrable Systems, 1-16, Progr. Nonlinear Differential Equations Appl., 26. Boston: Birkhäuser
    • (1997) Progr. Nonlinear Differential Equations Appl. , vol.26 , pp. 1-16
    • Alber, M.S.1    Luther, G.G.2    Marsden, J.E.3
  • 12
    • 0002589177 scopus 로고
    • Factorization of energy dependent Schrödinger operators: Miura maps and modified systems
    • Antonowicz, M. and Fordy, A. P. [1989]: Factorization of energy dependent Schrödinger operators: Miura maps and modified systems. Commun. Math. Phys. 124, no. 3, 465-486
    • (1989) Commun. Math. Phys. , vol.124 , Issue.3 , pp. 465-486
    • Antonowicz, M.1    Fordy, A.P.2
  • 13
    • 0000174121 scopus 로고    scopus 로고
    • Acoustic scattering and the extended Korteweg de Vries hierarchy
    • Beals, W., Sattinger, D., and Szmigielski, J. [1998]: Acoustic scattering and the extended Korteweg de Vries hierarchy. Adv. Math. 140, 190-206
    • (1998) Adv. Math. , vol.140 , pp. 190-206
    • Beals, W.1    Sattinger, D.2    Szmigielski, J.3
  • 15
    • 0034714658 scopus 로고    scopus 로고
    • Multipeakons and the classical moment
    • Beals, R., Sattinger, D.H. and Szmigielski, J. [2000]: Multipeakons and the classical moment. Adv. in Math. 154, no. 2, 229-257
    • (2000) Adv. in Math. , vol.154 , Issue.2 , pp. 229-257
    • Beals, R.1    Sattinger, D.H.2    Szmigielski, J.3
  • 17
    • 0007133485 scopus 로고    scopus 로고
    • Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products
    • Bobenko, A. I. and Suris, Y. B. [1999]: Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products. Lett. Math. Phys. 49, no. 1, 79-93
    • (1999) Lett. Math. Phys. , vol.49 , Issue.1 , pp. 79-93
    • Bobenko, A.I.1    Suris, Y.B.2
  • 18
    • 0032162250 scopus 로고    scopus 로고
    • Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies
    • Bulla, W., Gesztesy, F., Holden, H. and Teschl, G. [1998]: Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies. Mem. Am. Math. Soc. 135
    • (1998) Mem. Am. Math. Soc. , vol.135
    • Bulla, W.1    Gesztesy, F.2    Holden, H.3    Teschl, G.4
  • 19
    • 33746112384 scopus 로고    scopus 로고
    • Characteristic variables for a completely integrable shallow water equation
    • Boiti, M. et al. (eds.). Singapore: World Scientific
    • Camassa, R. [2000]: Characteristic variables for a completely integrable shallow water equation. In: Boiti, M. et al. (eds.) Nonlinearity, Integrability and All That: Twenty Years After NEEDS '79. Singapore: World Scientific
    • (2000) Nonlinearity, Integrability and All That: Twenty Years after NEEDS '79
    • Camassa, R.1
  • 20
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • Camassa, R., Holm, D.D. [1993]: An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661-1664
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 21
    • 56349110516 scopus 로고
    • A new integrable shallow water equation
    • Camassa, R., Holm, D.D. and Hyman, J.M. [1994]: A new integrable shallow water equation. Adv. Appl. Mech. 31, 1-33
    • (1994) Adv. Appl. Mech. , vol.31 , pp. 1-33
    • Camassa, R.1    Holm, D.D.2    Hyman, J.M.3
  • 22
    • 0000495444 scopus 로고
    • An integrable Hamiltonian system
    • Calogero, F. [1995]: An integrable Hamiltonian system. Phys. Lett. A 201, 306-310
    • (1995) Phys. Lett. A , vol.201 , pp. 306-310
    • Calogero, F.1
  • 23
    • 0030490914 scopus 로고    scopus 로고
    • Solvable quantum version of an integrable Hamiltonian system
    • Calogero, F. and Francoise, J.-P. [1996]: Solvable quantum version of an integrable Hamiltonian system. J. Math. Phys. 37 (6), 2863-2871
    • (1996) J. Math. Phys. , vol.37 , Issue.6 , pp. 2863-2871
    • Calogero, F.1    Francoise, J.-P.2
  • 24
    • 0007740237 scopus 로고
    • Stationary Harry-Dym's equation and its relation with geodesic on ellipsoid
    • Cewen, C. [1990]: Stationary Harry-Dym's equation and its relation with geodesic on ellipsoid. Acta Math. Sinica 6, 35-41
    • (1990) Acta Math. Sinica , vol.6 , pp. 35-41
    • Cewen, C.1
  • 26
    • 0010979902 scopus 로고
    • Finite-gap solutions of the Harry Dym equation
    • Dmitrieva, L.A. [1993a]: Finite-gap solutions of the Harry Dym equation. Phys. Lett. A 182, 65-70
    • (1993) Phys. Lett. A , vol.182 , pp. 65-70
    • Dmitrieva, L.A.1
  • 27
    • 21344482314 scopus 로고
    • The higher-times approach to multisoliton solutions of the Harry Dym equation
    • Dmitrieva, L.A. [1993b]: The higher-times approach to multisoliton solutions of the Harry Dym equation J. Phys. A 26, 6005-6020
    • (1993) J. Phys. A , vol.26 , pp. 6005-6020
    • Dmitrieva, L.A.1
  • 28
    • 0001349484 scopus 로고
    • 2 = [φ (x) + h]y
    • 2 = [φ (x) + h]y. Comptes rendus 168, 337-340
    • (1919) Comptes Rendus , vol.168 , pp. 337-340
    • Drach, M.1
  • 29
    • 34250407091 scopus 로고
    • Periodic problems for the Korteweg-de Vries equation in the class of finite-band potentials
    • Dubrovin, B.A. [1975]: Periodic problems for the Korteweg-de Vries equation in the class of finite-band potentials. Funct. Anal. Appl. 9, 215-223
    • (1975) Funct. Anal. Appl. , vol.9 , pp. 215-223
    • Dubrovin, B.A.1
  • 30
    • 84928007477 scopus 로고
    • Theta-functions and nonlinear equations
    • Dubrovin, B.A. [1981]: Theta-functions and nonlinear equations. Russ. Math. Surv. 36 (2), 11-92
    • (1981) Russ. Math. Surv. , vol.36 , Issue.2 , pp. 11-92
    • Dubrovin, B.A.1
  • 31
    • 0009577252 scopus 로고
    • Generalized theta functions and homoclinic varieties
    • Ehrenpreis, L., Gunning, R.C. (eds.). Proceedings, Bowdoin, Providence, R.I.: American Mathematical Society
    • Ercolani, N. [1987]: Generalized theta functions and homoclinic varieties. In: Ehrenpreis, L., Gunning, R.C. (eds.) Theta functions. Proceedings, Bowdoin. 87-100, Providence, R.I.: American Mathematical Society
    • (1987) Theta Functions , pp. 87-100
    • Ercolani, N.1
  • 32
    • 0042877956 scopus 로고    scopus 로고
    • Classical integrable systems related to generalized Jacobians
    • Fedorov, Yu. [1999]: Classical integrable systems related to generalized Jacobians. Acta Appl. Math. 55, 3, 151-201
    • (1999) Acta Appl. Math. , vol.55 , Issue.3 , pp. 151-201
    • Fedorov, Yu.1
  • 33
    • 0035735168 scopus 로고    scopus 로고
    • Ellipsoidal billiard with the quadratic potential
    • to appear
    • Fedorov, Yu. [2001]: Ellipsoidal billiard with the quadratic potential. Funct. Anal. Appl. (Russian) (to appear)
    • (2001) Funct. Anal. Appl. (Russian)
    • Fedorov, Yu.1
  • 34
    • 0033416562 scopus 로고    scopus 로고
    • Generalized Jacobians of spectral curves and completely integrable systems
    • Gavrilov, L. [1999]: Generalized Jacobians of spectral curves and completely integrable systems. Math. Z. 230, 487-508
    • (1999) Math. Z. , vol.230 , pp. 487-508
    • Gavrilov, L.1
  • 35
    • 0002587060 scopus 로고
    • New trace formulas for Schrödinger operators. Evolution equations
    • Baton Rouge, LA, 1992, New York: Dekker
    • Gesztesy, F. [1995]: New trace formulas for Schrödinger operators. Evolution equations (Baton Rouge, LA, 1992), Lecture Notes in Pure and Appl. Math., 168, New York: Dekker, pp. 201-221
    • (1995) Lecture Notes in Pure and Appl. Math. , vol.168 , pp. 201-221
    • Gesztesy, F.1
  • 36
    • 0002028453 scopus 로고
    • Trace formulas and conservation laws for nonlinear evolution equations
    • Gesztesy, F. and Holden, H. [1994]: Trace formulas and conservation laws for nonlinear evolution equations. Rev. Math. Phys. 6, 51-95 and 673
    • (1994) Rev. Math. Phys. , vol.6 , pp. 51-95
    • Gesztesy, F.1    Holden, H.2
  • 38
    • 0038950856 scopus 로고    scopus 로고
    • Dubrovin equations and integrable systems on hyperelliptic curves
    • to appear
    • Gesztesy, F. and Holden, H. [2001]: Dubrovin equations and integrable systems on hyperelliptic curves. Math. Scand. (to appear)
    • (2001) Math. Scand.
    • Gesztesy, F.1    Holden, H.2
  • 39
    • 0001124817 scopus 로고    scopus 로고
    • The KdV hierarchy and associated trace formulas. Recent developments in operator theory and its applications
    • Winnipeg, MB, 1994, Basel: Birkhäuser
    • Gesztesy, F., Ratnaseelan, R., and Teschl, G. [1996]: The KdV hierarchy and associated trace formulas. Recent developments in operator theory and its applications (Winnipeg, MB, 1994), 125-163, Oper. Theory Adv. Appl. 87, Basel: Birkhäuser
    • (1996) Oper. Theory Adv. Appl. , vol.87 , pp. 125-163
    • Gesztesy, F.1    Ratnaseelan, R.2    Teschl, G.3
  • 40
    • 0000452055 scopus 로고
    • On a completely integrable nonlinear hyperbolic variational equation
    • Hunter, J.K. and Zheng, Y.X. [1994]: On a completely integrable nonlinear hyperbolic variational equation. Physica D 79, 361-386
    • (1994) Physica D , vol.79 , pp. 361-386
    • Hunter, J.K.1    Zheng, Y.X.2
  • 43
    • 0001367543 scopus 로고
    • On an inverse scattering problem with an energy dependent potential
    • Jaulent, M. [1972]: On an inverse scattering problem with an energy dependent potential. Ann. Inst. H. Poincare A 17, 363-372
    • (1972) Ann. Inst. H. Poincare A , vol.17 , pp. 363-372
    • Jaulent, M.1
  • 44
    • 0001045583 scopus 로고
    • The inverse problem for the one-dimensional Schrödinger operator with an energy dependent potential
    • Jaulent, M. and Jean, C. [1976]: The inverse problem for the one-dimensional Schrödinger operator with an energy dependent potential. Ann. Inst. H. Poincare A. I, II 25, 105-118, 119-137
    • (1976) Ann. Inst. H. Poincare A. I, II , vol.25 , pp. 105-118
    • Jaulent, M.1    Jean, C.2
  • 47
    • 84941484100 scopus 로고
    • Geodesics on quadrics and mechanical problem of C. Neumann
    • Knörrer, H. [1982]: Geodesics on quadrics and mechanical problem of C. Neumann. J. Reine Angew. Math. 334, 69-78
    • (1982) J. Reine Angew. Math. , vol.334 , pp. 69-78
    • Knörrer, H.1
  • 49
    • 0038363162 scopus 로고
    • Nonlinear wave equations
    • Moser, J. (eds.) Dynamical Systems, Theory and Applications, New York: Springer
    • Kruskal, M.D. [1975]: Nonlinear wave equations. In: Moser, J. (eds.) Dynamical Systems, Theory and Applications. Lecture Notes in Physics 38, New York: Springer
    • (1975) Lecture Notes in Physics , vol.38
    • Kruskal, M.D.1
  • 50
    • 0040134967 scopus 로고
    • Introduction to the theory of Abelian functions
    • English version. Providence, RI: American Mathematical Society, 1992
    • Markushevich, A. I. [1977]: Introduction to the Theory of Abelian Functions. English version: Translations of Mathematical Monographs, 96. Providence, RI: American Mathematical Society, 1992
    • (1977) Translations of Mathematical Monographs , vol.96
    • Markushevich, A.I.1
  • 51
    • 0032476963 scopus 로고    scopus 로고
    • Mulltisymplectic geometry, variational integrators and nonlinear PDEs
    • Marsden, J. E., Patrick, G.W., and Shkoller, S. [1998]: Mulltisymplectic geometry, variational integrators and nonlinear PDEs, Commun. Math. Phys. 199, 351-395
    • (1998) Commun. Math. Phys. , vol.199 , pp. 351-395
    • Marsden, J.E.1    Patrick, G.W.2    Shkoller, S.3
  • 52
    • 0033228880 scopus 로고    scopus 로고
    • Discrete Euler-Poincare and Lie-Poisson equations
    • Marsden, J. E., Pekarsky, S., and Shkoller, S. [1999]: Discrete Euler-Poincare and Lie-Poisson equations. Nonlinearity 12, 1647-1662
    • (1999) Nonlinearity , vol.12 , pp. 1647-1662
    • Marsden, J.E.1    Pekarsky, S.2    Shkoller, S.3
  • 53
    • 0003274786 scopus 로고    scopus 로고
    • Introduction to mechanics and symmetry
    • Berlin-Heidelberg-New York: Springer-Verlag
    • Marsden, J. E. and Ratiu, T.S. [1999]: Introduction to Mechanics and Symmetry. Texts in Applied Mathematics, 17, Berlin-Heidelberg-New York: Springer-Verlag
    • (1999) Texts in Applied Mathematics , vol.17
    • Marsden, J.E.1    Ratiu, T.S.2
  • 54
    • 0033415933 scopus 로고    scopus 로고
    • A shallow water equation on the circle
    • McKean, H.P. and Constantin, A. [1999]: A shallow water equation on the circle. Comm. Pure Appl. Math. Vol LII, 949-982
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 949-982
    • McKean, H.P.1    Constantin, A.2
  • 55
    • 0000008977 scopus 로고
    • Discrete versions of some classical integrable systems and factorization of matrix polynomials
    • Moser, J. and Veselov, A.P. [1991]: Discrete versions of some classical integrable systems and factorization of matrix polynomials. Commum. Math. Phys. 139, 217-243
    • (1991) Commum. Math. Phys. , vol.139 , pp. 217-243
    • Moser, J.1    Veselov, A.P.2
  • 57
    • 85017290391 scopus 로고    scopus 로고
    • Algebraic-geometrical solutions of the Harry-Dym equations
    • Novikov D.P. [1999]: Algebraic-geometrical solutions of the Harry-Dym equations. Sibirskii Matematicheskii Zhurnal, 40, 159-163, (Russian) English transl. in: Siberian Math. Journal, 40, 136-140
    • (1999) Sibirskii Matematicheskii Zhurnal , vol.40 , pp. 159-163
    • Novikov, D.P.1
  • 58
    • 0039543489 scopus 로고    scopus 로고
    • (Russian) English transl.
    • Novikov D.P. [1999]: Algebraic-geometrical solutions of the Harry-Dym equations. Sibirskii Matematicheskii Zhurnal, 40, 159-163, (Russian) English transl. in: Siberian Math. Journal, 40, 136-140
    • Siberian Math. Journal , vol.40 , pp. 136-140
  • 59
    • 84972582970 scopus 로고
    • Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation
    • Previato, E. [1995]: Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation. Duke Math. J. 52, 329-377
    • (1995) Duke Math. J. , vol.52 , pp. 329-377
    • Previato, E.1
  • 60
    • 0007844274 scopus 로고
    • Mechanical systems related to the Schrödinger spectral problem
    • Rauch-Wojciechowski, S. [1995]: Mechanical systems related to the Schrödinger spectral problem. Chaos, Solitons & Fractals 5, 2235-2259
    • (1995) Chaos, Solitons & Fractals , vol.5 , pp. 2235-2259
    • Rauch-Wojciechowski, S.1
  • 62
    • 0040728836 scopus 로고
    • Stratification of hyperelliptic Jacobians and the Sato Grassmannian
    • Vanhaecke, P. [1995]: Stratification of hyperelliptic Jacobians and the Sato Grassmannian. Acta Appl. Math. 40, 143-172
    • (1995) Acta Appl. Math. , vol.40 , pp. 143-172
    • Vanhaecke, P.1
  • 63
    • 0002859047 scopus 로고
    • Integrable discrete-time systems and difference operators
    • Veselov, A.P. [1988]: Integrable discrete-time systems and difference operators. Funct. An. and Appl. 22, 83-94
    • (1988) Funct. An. and Appl. , vol.22 , pp. 83-94
    • Veselov, A.P.1
  • 65
    • 0001098290 scopus 로고
    • Cusp soliton of a new integrable nonlinear evolution equation
    • Wadati, M., Ichikawa, Y.H., and Shimizu, T. [1980]: Cusp soliton of a new integrable nonlinear evolution equation. Prog. Theor. Phys. 64, 1959-1967
    • (1980) Prog. Theor. Phys. , vol.64 , pp. 1959-1967
    • Wadati, M.1    Ichikawa, Y.H.2    Shimizu, T.3
  • 66
    • 0041127089 scopus 로고
    • Über die geodätischen linien auf dreiachsigen ellipsoid
    • Weierstrass, K. [1884]: Über die geodätischen Linien auf dreiachsigen Ellipsoid, Math. Werke I, 257-266
    • (1884) Math. Werke I , pp. 257-266
    • Weierstrass, K.1
  • 67
    • 0031210701 scopus 로고    scopus 로고
    • Mechanical integrators derived from a discrete variational principle
    • Wendlandt, J.M. and Marsden, J.E. [1997]: Mechanical integrators derived from a discrete variational principle. Physica D 106, 223-246
    • (1997) Physica D , vol.106 , pp. 223-246
    • Wendlandt, J.M.1    Marsden, J.E.2
  • 68
    • 0003591959 scopus 로고
    • Cambridge: Cambridge University Press, 1904; 4th Ed., 1937 (reprinted by Dover 1944, and Cambridge University 1988)
    • Whittaker, E.T. [1937]: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge: Cambridge University Press, 1904; 4th Ed., 1937 (reprinted by Dover 1944, and Cambridge University 1988)
    • (1937) A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
    • Whittaker, E.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.