메뉴 건너뛰기




Volumn 365, Issue 1858, 2007, Pages 2299-2312

The string density problem and the Camassa-Hojm equation

Author keywords

Camassa Holm equation; Multi peakon; Spectral problem; String density problem

Indexed keywords


EID: 34548275575     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2007.2010     Document Type: Article
Times cited : (18)

References (38)
  • 1
    • 0001344780 scopus 로고
    • Inverse problem for the vibrating beam in the free-clamped configuration
    • doi:10.1098/rsta.1982.0012
    • Barcilon, V. 1982 Inverse problem for the vibrating beam in the free-clamped configuration. Phil. Trans. R. Soc. A 304, 211-251. (doi:10.1098/rsta.1982.0012)
    • (1982) Phil. Trans. R. Soc. A , vol.304 , pp. 211-251
    • Barcilon, V.1
  • 2
    • 0000174121 scopus 로고    scopus 로고
    • Beals, R., Sattinger, D., Sattinger, H.k Szmigielski, J. 1998 Acoustic scattering and the extended Korteweg-de Vries hierarchy. Adv. Math. 140, 190-206. (doi:10.1006/aima.1998.1768)
    • Beals, R., Sattinger, D., Sattinger, H.k Szmigielski, J. 1998 Acoustic scattering and the extended Korteweg-de Vries hierarchy. Adv. Math. 140, 190-206. (doi:10.1006/aima.1998.1768)
  • 3
    • 18044392342 scopus 로고    scopus 로고
    • Multi-peakons and a theorem of Stieltjes
    • doi: 10.1088/0266-5611/15/1/001
    • Beals, R., Sattinger, D., Sattinger, H. & Szmigielski, J. 1999 Multi-peakons and a theorem of Stieltjes. Inverse Probl. 15, L1-L4. (doi: 10.1088/0266-5611/15/1/001)
    • (1999) Inverse Probl , vol.15
    • Beals, R.1    Sattinger, D.2    Sattinger, H.3    Szmigielski, J.4
  • 4
    • 0034714658 scopus 로고    scopus 로고
    • Multipeakons and the classical moment problem
    • doi:10.1006/aima.1999.1883
    • Beals, R., Sattinger, D., Sattinger, H. & Szmigielski, J. 2000 Multipeakons and the classical moment problem. Adv. Math. 154, 229-257. (doi:10.1006/aima.1999.1883)
    • (2000) Adv. Math , vol.154 , pp. 229-257
    • Beals, R.1    Sattinger, D.2    Sattinger, H.3    Szmigielski, J.4
  • 5
    • 0035526709 scopus 로고    scopus 로고
    • Beals, R., Sattinger, D., Sattinger, H. & Szmigielski, J. 2001 Peakons, strings, and the finite Toda lattice. Commun. Pure Appl. Math. 54, 91-106. (doi:10.1002/1097-0312(200101)54:<91::AID-CPA4>3.0. CO;2-O)
    • Beals, R., Sattinger, D., Sattinger, H. & Szmigielski, J. 2001 Peakons, strings, and the finite Toda lattice. Commun. Pure Appl. Math. 54, 91-106. (doi:10.1002/1097-0312(200101)54:<91::AID-CPA4>3.0. CO;2-O)
  • 6
    • 33646975016 scopus 로고
    • Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe
    • doi:10.1007/BF02421600
    • Borg, G. 1946 Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Acta Math. 78, 1-96. (doi:10.1007/BF02421600)
    • (1946) Acta Math , vol.78 , pp. 1-96
    • Borg, G.1
  • 7
    • 0041760859 scopus 로고    scopus 로고
    • Characteristics and the initial value problem of a completely integrable shallow water equation
    • Camassa, R. 2003 Characteristics and the initial value problem of a completely integrable shallow water equation. Discrete Cont. Dyn. Syst. Ser. B 3, 115-139.
    • (2003) Discrete Cont. Dyn. Syst. Ser. B , vol.3 , pp. 115-139
    • Camassa, R.1
  • 8
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • doi:10.1103/PhysRevLett.71.1661
    • Camassa, R. & Holm, D. 1993 An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661-1664. (doi:10.1103/PhysRevLett.71.1661)
    • (1993) Phys. Rev. Lett , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.2
  • 9
    • 0000684999 scopus 로고    scopus 로고
    • On the inverse spectral problem for the Camassa-Holm equation
    • doi:10.1006/jfan.1997. 3231
    • Constantin, A. 1998 On the inverse spectral problem for the Camassa-Holm equation. J. Funct. Anal. 155, 352-363. (doi:10.1006/jfan.1997. 3231)
    • (1998) J. Funct. Anal , vol.155 , pp. 352-363
    • Constantin, A.1
  • 10
    • 34447130573 scopus 로고    scopus 로고
    • On the scattering problem for the Camassa-Holm equation
    • doi:10.1098/rspa.2000. 0701
    • Constantin, A. 2001 On the scattering problem for the Camassa-Holm equation. Proc. R. Soc. A 457, 953-970. (doi:10.1098/rspa.2000. 0701)
    • (2001) Proc. R. Soc. A , vol.457 , pp. 953-970
    • Constantin, A.1
  • 11
    • 0037429683 scopus 로고    scopus 로고
    • On the inverse scattering approach for an integrable shallow water wave equation
    • doi:10.1016/S0375-9601(03)00109-9
    • Constantin, A. & Lenells, J. 2003a On the inverse scattering approach for an integrable shallow water wave equation. Phys. Lett. A 308, 432-436. (doi:10.1016/S0375-9601(03)00109-9)
    • (2003) Phys. Lett. A , vol.308 , pp. 432-436
    • Constantin, A.1    Lenells, J.2
  • 12
    • 0042023771 scopus 로고    scopus 로고
    • 20036 On the inverse scattering approach to the Camassa-Holm equation
    • doi: 10.2991/jnmp.2003.10.3.1
    • Constantin, A. & Lenells, J. 20036 On the inverse scattering approach to the Camassa-Holm equation. J. Nonlin. Math. Phys. 10, 252-255. (doi: 10.2991/jnmp.2003.10.3.1)
    • J. Nonlin. Math. Phys , vol.10 , pp. 252-255
    • Constantin, A.1    Lenells, J.2
  • 13
    • 0033415933 scopus 로고    scopus 로고
    • Constantin, A. & McKean, H. P. 1999 A shallow water equation on the circle. Commun. Pure Appl. Math. 52, 949-982. (doi:10.1002/(SICI) 1097-0312(199908)52:8<949::AID-CPA3>3.0. CO;2-D)
    • Constantin, A. & McKean, H. P. 1999 A shallow water equation on the circle. Commun. Pure Appl. Math. 52, 949-982. (doi:10.1002/(SICI) 1097-0312(199908)52:8<949::AID-CPA3>3.0. CO;2-D)
  • 14
    • 85020774114 scopus 로고    scopus 로고
    • Dym, H. & Kravitsky, N. 1978a On recovering the mass distribution of a string from its spectral function. In Topics in functional analysis, 3 (eds I. Gohberg & M. Kac). Advances in Mathematics Supplementary Studies, pp. 45-90. New York, NY: Academic Press.
    • Dym, H. & Kravitsky, N. 1978a On recovering the mass distribution of a string from its spectral function. In Topics in functional analysis, vol. 3 (eds I. Gohberg & M. Kac). Advances in Mathematics Supplementary Studies, pp. 45-90. New York, NY: Academic Press.
  • 15
    • 34250277566 scopus 로고    scopus 로고
    • 19786 On the inverse spectral problem for the string equation
    • doi:10.1007/BF01690986
    • Dym, H. & Kravitsky, N. 19786 On the inverse spectral problem for the string equation. Integr. Equat. Oper. Th. 1, 270-277. (doi:10.1007/BF01690986)
    • Integr. Equat. Oper. Th , vol.1 , pp. 270-277
    • Dym, H.1    Kravitsky, N.2
  • 17
    • 0001025045 scopus 로고
    • The Lie algebra structure of nonlinear evolution equations and infinite dimensional abelian symmetry groups
    • doi:10.1143/PTP.65.861
    • Fuchssteiner, B. 1981 The Lie algebra structure of nonlinear evolution equations and infinite dimensional abelian symmetry groups. Progr. Theor. Phys. 65, 861-880. (doi:10.1143/PTP.65.861)
    • (1981) Progr. Theor. Phys , vol.65 , pp. 861-880
    • Fuchssteiner, B.1
  • 18
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • doi:10.1016/0167-2789(81)90004-X
    • Fuchssteiner, B. & Fokas, A. S. 1981 Symplectic structures, their Bäcklund transformations and hereditary symmetries. Physica D 4, 47-66. (doi:10.1016/0167-2789(81)90004-X)
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 19
    • 0001458591 scopus 로고
    • On the determination of a differential equation from its spectral function
    • Gel'fand, I. M. & Levitan, B. M. 1951 On the determination of a differential equation from its spectral function. Izvestiya Akad. Nauk SSSR. Ser. Mat. 15, 309-360.
    • (1951) Izvestiya Akad. Nauk SSSR. Ser. Mat , vol.15 , pp. 309-360
    • Gel'fand, I.M.1    Levitan, B.M.2
  • 21
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, Korteweg-de Vries and related models for water waves
    • doi: 10.1017/S0022112001007224
    • Johnson, R. S. 2002 Camassa-Holm, Korteweg-de Vries and related models for water waves. J. Fluid Mech. 455, 63-82. (doi: 10.1017/S0022112001007224)
    • (2002) J. Fluid Mech , vol.455 , pp. 63-82
    • Johnson, R.S.1
  • 22
    • 1342300742 scopus 로고    scopus 로고
    • On solutions of the Camassa-Holm equation
    • doi: 10.1098/rspa.2002.1078
    • Johnson, R. S. 2003 On solutions of the Camassa-Holm equation. Proc. R. Soc. A 459, 1687-1708. (doi: 10.1098/rspa.2002.1078)
    • (2003) Proc. R. Soc. A , vol.459 , pp. 1687-1708
    • Johnson, R.S.1
  • 23
    • 0002877790 scopus 로고
    • On the spectral functions of the string
    • Kac, I. S. & Krein, M. G. 1974 On the spectral functions of the string. Am. Math. Soc. Transi. 103, 19-102.
    • (1974) Am. Math. Soc. Transi , vol.103 , pp. 19-102
    • Kac, I.S.1    Krein, M.G.2
  • 24
    • 10044244825 scopus 로고    scopus 로고
    • Inverse spectral problem for the periodic Camassa-Holm equation
    • doi:10.2991/jnmp.2004.11.4.6
    • Korotyaev, E. 2004 Inverse spectral problem for the periodic Camassa-Holm equation. J. Nonlin. Math. Phys. 11, 499-507. (doi:10.2991/jnmp.2004.11.4.6)
    • (2004) J. Nonlin. Math. Phys , vol.11 , pp. 499-507
    • Korotyaev, E.1
  • 25
    • 0001332671 scopus 로고
    • Determination of the density of a nonhomogeneous symmetric cord by its frequency spectrum
    • Kreǐn, M. G. 1951 Determination of the density of a nonhomogeneous symmetric cord by its frequency spectrum. Doklady Akad. Nauk SSSR (NS.) 76, 345-348.
    • (1951) Doklady Akad. Nauk SSSR (NS.) , vol.76 , pp. 345-348
    • Kreǐn, M.G.1
  • 26
    • 0010834255 scopus 로고
    • On a generalization of investigations of Stieltjes
    • Kreǐn, M. G. 1952a On a generalization of investigations of Stieltjes. Doklady Akad. Nauk SSSR (N. S.) 87, 881-884.
    • (1952) Doklady Akad. Nauk SSSR (N. S.) , vol.87 , pp. 881-884
    • Kreǐn, M.G.1
  • 27
    • 0001682920 scopus 로고    scopus 로고
    • 19526 On inverse problems for a nonhomogeneous cord
    • Kreǐn, M. G. 19526 On inverse problems for a nonhomogeneous cord. Doklady Akad. Nauk SSSR (NS.) 82, 669-672.
    • Doklady Akad. Nauk SSSR (NS.) , vol.82 , pp. 669-672
    • Kreǐn, M.G.1
  • 28
    • 0040106527 scopus 로고
    • On some cases of effective determination of the density of an inhomogeneous cord from its spectral function
    • Kreǐn, M. G. 1953 On some cases of effective determination of the density of an inhomogeneous cord from its spectral function. Doklady Akad. Nauk SSSR (N.S.) 93, 617-620.
    • (1953) Doklady Akad. Nauk SSSR (N.S.) , vol.93 , pp. 617-620
    • Kreǐn, M.G.1
  • 29
    • 0039412671 scopus 로고
    • On a method of effective solution of an inverse boundary problem
    • Kreǐn, M. G. 1954 On a method of effective solution of an inverse boundary problem. Doklady Akad. Nauk SSSR (NS.) 94, 987-990.
    • (1954) Doklady Akad. Nauk SSSR (NS.) , vol.94 , pp. 987-990
    • Kreǐn, M.G.1
  • 30
    • 0036434830 scopus 로고    scopus 로고
    • The scattering approach for the Camassa-Holm equation
    • doi:10.2991/jnmp.2002.9.4.2
    • Lenells, J. 2002 The scattering approach for the Camassa-Holm equation. J. Nonlin. Math. Phys. 9, 389-393. (doi:10.2991/jnmp.2002.9.4.2)
    • (2002) J. Nonlin. Math. Phys , vol.9 , pp. 389-393
    • Lenells, J.1
  • 31
    • 13244273595 scopus 로고    scopus 로고
    • The correspondence between KdV and Camassa-Holm
    • doi:10.1155/S1073792804142451
    • Lenells, J. 2004 The correspondence between KdV and Camassa-Holm. Int. Math. Res. Not. 71, 3797-3811. (doi:10.1155/S1073792804142451)
    • (2004) Int. Math. Res. Not , vol.71 , pp. 3797-3811
    • Lenells, J.1
  • 32
    • 34548281718 scopus 로고    scopus 로고
    • Factorization problem on the Hubert-Schmidt group and the Camassa-Holm equation
    • Li, L. C. 2005 Factorization problem on the Hubert-Schmidt group and the Camassa-Holm equation. Mittag-Leffler Preprints 19.
    • (2005) Mittag-Leffler Preprints , vol.19
    • Li, L.C.1
  • 33
    • 0000861291 scopus 로고
    • On reconstruction of the potential energy from phases of the scattered waves
    • Marěenko, V. A. 1955 On reconstruction of the potential energy from phases of the scattered waves. Doklady Akad. Nauka 104, 695-698.
    • (1955) Doklady Akad. Nauka , vol.104 , pp. 695-698
    • Marěenko, V.A.1
  • 34
    • 2442552977 scopus 로고    scopus 로고
    • The Liouville correspondence between the Korteweg-de Vries and the Camassa-Holm hierarchies
    • doi:10.1002/cpa.10083
    • McKean, H. P. 2003 The Liouville correspondence between the Korteweg-de Vries and the Camassa-Holm hierarchies. Commun. Pure. Appl. Math. 56, 998-1015. (doi:10.1002/cpa.10083)
    • (2003) Commun. Pure. Appl. Math , vol.56 , pp. 998-1015
    • McKean, H.P.1
  • 35
    • 34347230069 scopus 로고
    • Three integrable Hamiltonian systems connected with isospectral deformations
    • doi:10.1016/0001-8708(75)90151-6
    • Moser, J. 1975 Three integrable Hamiltonian systems connected with isospectral deformations. Adv. Math. 16, 197-220. (doi:10.1016/0001-8708(75)90151-6)
    • (1975) Adv. Math , vol.16 , pp. 197-220
    • Moser, J.1
  • 36
    • 0002593008 scopus 로고
    • Recherches sur les fractions continues
    • Stieltjes, T. J. 1894 Recherches sur les fractions continues. Ann. Fac. Sci. Toulouse 8, 1-122.
    • (1894) Ann. Fac. Sci. Toulouse , vol.8 , pp. 1-122
    • Stieltjes, T.J.1
  • 37
    • 34250248977 scopus 로고
    • Systems of Toda type, inverse spectral problems, and representation theory
    • doi:10.1007/BF01390312
    • Symes, W. W. 1980 Systems of Toda type, inverse spectral problems, and representation theory, Invent. Math. 59, 13-51. (doi:10.1007/BF01390312)
    • (1980) Invent. Math , vol.59 , pp. 13-51
    • Symes, W.W.1
  • 38
    • 0000434148 scopus 로고
    • The QR-algorithm and scattering for the finite nonperiodic Toda lattice
    • doi:10.1016/0167-2789(82)90069-0
    • Symes, W. W. 1981 The QR-algorithm and scattering for the finite nonperiodic Toda lattice. Physica D 4, 275-280. (doi:10.1016/0167-2789(82)90069-0)
    • (1981) Physica D , vol.4 , pp. 275-280
    • Symes, W.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.