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Volumn 11, Issue 1, 2005, Pages 37-98

Birkhoff coordinates for KdV on phase spaces of distributions

Author keywords

KdV; Low regularity solutions of non linear PDE; Normal forms

Indexed keywords


EID: 27644537062     PISSN: 10221824     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00029-005-0009-6     Document Type: Article
Times cited : (18)

References (35)
  • 1
    • 0001778712 scopus 로고    scopus 로고
    • On the Korteweg - De Vries equation: Frequencies and initial value problem
    • D. Bättig, T. Kappeler and B. Mityagin. On the Korteweg - de Vries equation: frequencies and initial value problem. Pacific J. Math. 181 (1997), 1-55.
    • (1997) Pacific J. Math. , vol.181 , pp. 1-55
    • Bättig, D.1    Kappeler, T.2    Mityagin, B.3
  • 2
    • 84974003856 scopus 로고
    • On the symplectic structure of the phase space for periodic KdV, Toda, and defocusing NLS
    • D. Bättig, A. Bloch, J.-C. Guillot and T. Rappeler. On the symplectic structure of the phase space for periodic KdV, Toda, and defocusing NLS. Duke Math. J. 79 (1995), 549-604.
    • (1995) Duke Math. J. , vol.79 , pp. 549-604
    • Bättig, D.1    Bloch, A.2    Guillot, J.-C.3    Rappeler, T.4
  • 5
    • 0000044382 scopus 로고    scopus 로고
    • Periodic Korteweg - De Vries equation with measures as initial data
    • J. Bourgain. Periodic Korteweg - de Vries equation with measures as initial data. Sel. Math. 3 (1997), 115-159.
    • (1997) Sel. Math. , vol.3 , pp. 115-159
    • Bourgain, J.1
  • 7
    • 84990619700 scopus 로고
    • Solution of the inverse spectral problem for an impedance with integrable derivative I
    • C. Coleman and J. McLaughlin. Solution of the Inverse Spectral Problem for an Impedance with Integrable Derivative I. Comm. Pure. Appl. Math. 46 (1993), 145-184.
    • (1993) Comm. Pure. Appl. Math. , vol.46 , pp. 145-184
    • Coleman, C.1    McLaughlin, J.2
  • 8
    • 84990580984 scopus 로고
    • Solution of the inverse spectral problem for an impedance with integrable derivative II
    • C. Coleman and J. McLaughlin. Solution of the Inverse Spectral Problem for an Impedance with Integrable Derivative II. Comm. Pure Appl. Math. 46 (1993), 185-212.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 185-212
    • Coleman, C.1    McLaughlin, J.2
  • 9
    • 0038806261 scopus 로고    scopus 로고
    • Sharp global well-posedness for KdV and modified KdV on ℝ and double struct T sign
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao. Sharp global well-posedness for KdV and modified KdV on ℝ and double struct T sign. J. Amer. Math. Soc. 16 (2003), no. 3, 705-749.
    • (2003) J. Amer. Math. Soc. , vol.16 , Issue.3 , pp. 705-749
    • Colliander, J.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 10
    • 0001037331 scopus 로고
    • Canonically conjugate variables for the Korteweg - De vries equation and Toda lattice with periodic boundary conditions
    • H. Flaschka and D. McLaughlin. Canonically conjugate variables for the Korteweg - de Vries equation and Toda lattice with periodic boundary conditions. Progress of Theor. Phys. 55 (1976), 438-456.
    • (1976) Progress of Theor. Phys. , vol.55 , pp. 438-456
    • Flaschka, H.1    McLaughlin, D.2
  • 11
    • 8644231838 scopus 로고    scopus 로고
    • A note on gaps of Hill's equation
    • B. Grébert, T. Kappeler and J. Pöschel. A note on gaps of Hill's equation. IMRN 50 (2004), 2703-2717.
    • (2004) IMRN , vol.50 , pp. 2703-2717
    • Grébert, B.1    Kappeler, T.2    Pöschel, J.3
  • 12
    • 51249174723 scopus 로고
    • Convergence of Birkhoff normal forms for integrable systems
    • H. Ito. Convergence of Birkhoff normal forms for integrable systems. Comment. Math. Helv. 64 (1989), 412-461.
    • (1989) Comment. Math. Helv. , vol.64 , pp. 412-461
    • Ito, H.1
  • 13
    • 0035540786 scopus 로고    scopus 로고
    • On Birkhoff coordinates for KdV
    • T. Kappeler and M. Makarov. On Birkhoff coordinates for KdV. Ann. H. Poincaré 2 (2001), 807-856.
    • (2001) Ann. H. Poincaré , vol.2 , pp. 807-856
    • Kappeler, T.1    Makarov, M.2
  • 14
    • 0035527618 scopus 로고    scopus 로고
    • Estimates for periodic and dirichlet eigenvalues of the schrödinger operator
    • T. Kappeler and B. Mityagin. Estimates for periodic and Dirichlet eigenvalues of the Schrödinger operator. Siam J. Math. Anal. 33 (2001), 113-152.
    • (2001) Siam J. Math. Anal. , vol.33 , pp. 113-152
    • Kappeler, T.1    Mityagin, B.2
  • 15
    • 0035922968 scopus 로고    scopus 로고
    • Estimates for periodic and dirichlet eigenvalues of the schrödinger operator with singular potentials
    • T. Kappeler and C. Möhr. Estimates for periodic and Dirichlet eigenvalues of the Schrödinger operator with singular potentials. J. Funct. Anal. 186 (2001), 62-91.
    • (2001) J. Funct. Anal. , vol.186 , pp. 62-91
    • Kappeler, T.1    Möhr, C.2
  • 19
    • 3142724886 scopus 로고    scopus 로고
    • abridged version
    • abridged version in Pliska Stud. Math. Bulgar. 15 (2003), 171-188.
    • (2003) Pliska Stud. Math. Bulgar. , vol.15 , pp. 171-188
  • 22
    • 0030528276 scopus 로고    scopus 로고
    • A bilinear estimate with applications to the KdV equations
    • C. Kenig, P. Ponce and L. Vega. A bilinear estimate with applications to the KdV equations. J. Amer. Math. Soc. 9 (1996), 573-603.
    • (1996) J. Amer. Math. Soc. , vol.9 , pp. 573-603
    • Kenig, C.1    Ponce, P.2    Vega, L.3
  • 23
    • 0037431270 scopus 로고    scopus 로고
    • Periodic weighted operators
    • E. Korotyaev. Periodic weighted operators. J. Differential Equations 189 (2003), 461-486.
    • (2003) J. Differential Equations , vol.189 , pp. 461-486
    • Korotyaev, E.1
  • 24
    • 0000243017 scopus 로고    scopus 로고
    • Inverse problem for weighted operators
    • E. Korotyaev. Inverse problem for weighted operators. J. Funct. Anal. 170 (2000), 188-218.
    • (2000) J. Funct. Anal. , vol.170 , pp. 188-218
    • Korotyaev, E.1
  • 25
    • 0041332954 scopus 로고    scopus 로고
    • Characterization of the spectrum for schrödinger operator with periodic distributions
    • E. Korotyaev. Characterization of the spectrum for Schrödinger operator with periodic distributions. IMRN 37 (2003) 2019-2031.
    • (2003) IMRN , vol.37 , pp. 2019-2031
    • Korotyaev, E.1
  • 26
    • 0036400285 scopus 로고    scopus 로고
    • Invariance principle for inverse problems
    • E. Korotyaev. Invariance principle for inverse problems. IMRN 38 (2002), 2007-2020.
    • (2002) IMRN , vol.38 , pp. 2007-2020
    • Korotyaev, E.1
  • 27
    • 0003109280 scopus 로고
    • The basic propositions of the theory of λ-zones of stability of a canonical system of linear differential equations with periodic coefficients
    • Izdat. Akad. Nauk SSSR, Moscow
    • M. Krein. The basic propositions of the theory of λ-zones of stability of a canonical system of linear differential equations with periodic coefficients. In: In memory of A. A. Andronov. 413-498. Izdat. Akad. Nauk SSSR, Moscow, 1955.
    • (1955) In Memory of A. A. Andronov , pp. 413-498
    • Krein, M.1
  • 28
    • 0040758102 scopus 로고    scopus 로고
    • Action-angle variables for the cubic schrödinger equation
    • H. McKean and K. Vaninsky. Action-angle variables for the cubic Schrödinger equation. Commun. Pure Appl. Math. 50 (1997), 489-562.
    • (1997) Commun. Pure Appl. Math. , vol.50 , pp. 489-562
    • McKean, H.1    Vaninsky, K.2
  • 29
    • 27644595744 scopus 로고    scopus 로고
    • Thesis. University of Zürich
    • C. Möhr. Thesis. University of Zürich, 2001.
    • (2001)
    • Möhr, C.1
  • 30
    • 0002945849 scopus 로고
    • Lectures on Hamiltonian systems
    • J. Moser. Lectures on Hamiltonian Systems. Mem. Amer. Math. Soc. 81 (1968), 1-60.
    • (1968) Mem. Amer. Math. Soc. , vol.81 , pp. 1-60
    • Moser, J.1
  • 32
    • 0011396824 scopus 로고
    • Über die existenz einer normalform analytischer hamiltonscher differentialgleichungen in der nähe einer gleichgewichtslösung
    • C. L. Siegel. Über die Existenz einer Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung. Math. Ann. 128 (1954), 144-170.
    • (1954) Math. Ann. , vol.128 , pp. 144-170
    • Siegel, C.L.1
  • 34
    • 0000132941 scopus 로고
    • Sur certains systèmes dynamiques séparables
    • J. Vey. Sur certains systèmes dynamiques séparables. Amer. J. Math. 100 (1978), 591-614.
    • (1978) Amer. J. Math. , vol.100 , pp. 591-614
    • Vey, J.1
  • 35
    • 0036327480 scopus 로고    scopus 로고
    • Convergence versus integrability in Birkhoff normal form
    • N. T. Zung. Convergence versus integrability in Birkhoff normal form. Math. Res. Lett. 9 (2-3) (2002), 217-228.
    • (2002) Math. Res. Lett. , vol.9 , Issue.2-3 , pp. 217-228
    • Zung, N.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.