메뉴 건너뛰기




Volumn , Issue 71, 2004, Pages 3797-3811

The correspondence between KdV and Camassa-Holm

Author keywords

[No Author keywords available]

Indexed keywords


EID: 13244273595     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/S1073792804142451     Document Type: Article
Times cited : (50)

References (37)
  • 1
    • 0000174121 scopus 로고    scopus 로고
    • Acoustic scattering and the extended Korteweg-de Vries hierarchy
    • R. Beals, D. Sattinger, and J. Szmigielski, Acoustic scattering and the extended Korteweg-de Vries hierarchy, Adv. Math. 140 (1998), no. 2, 190-206.
    • (1998) Adv. Math. , vol.140 , Issue.2 , pp. 190-206
    • Beals, R.1    Sattinger, D.2    Szmigielski, J.3
  • 2
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71 (1993), no. 11, 1661-1664.
    • (1993) Phys. Rev. Lett. , vol.71 , Issue.11 , pp. 1661-1664
    • Camassa, R.1    Holm, D.2
  • 3
    • 0038806261 scopus 로고    scopus 로고
    • Sharp global well-posedness for KdV and modified KdV on R and T
    • J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao, Sharp global well-posedness for KdV and modified KdV on R and T, 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
  • 4
    • 0000684999 scopus 로고    scopus 로고
    • On the inverse spectral problem for the Camassa-Holm equation
    • A. Constantin, On the inverse spectral problem for the Camassa-Holm equation, J. Funct. Anal. 155 (1998), no. 2, 352-363.
    • (1998) J. Funct. Anal. , vol.155 , Issue.2 , pp. 352-363
    • Constantin, A.1
  • 5
    • 0034415062 scopus 로고    scopus 로고
    • Existence of permanent and breaking waves for a shallow water equation: A geometric approach
    • _, Existence of permanent and breaking waves for a shallow water equation: a geometric approach, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 2, 321-362.
    • (2000) Ann. Inst. Fourier (Grenoble) , vol.50 , Issue.2 , pp. 321-362
  • 6
    • 34447130573 scopus 로고    scopus 로고
    • On the scattering problem for the Camassa-Holm equation
    • _, On the scattering problem for the Camassa-Holm equation, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 457 (2001), no. 2008, 953-970.
    • (2001) R. Soc. Lond. Proc. Ser. a Math. Phys. Eng. Sci. , vol.457 , Issue.2008 , pp. 953-970
  • 7
    • 85129402022 scopus 로고    scopus 로고
    • Global existence and blow-up for a shallow water equation
    • A. Constantin and J. Escher, Global existence and blow-up for a shallow water equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 26 (1998), no. 2, 303-328.
    • (1998) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.26 , Issue.2 , pp. 303-328
    • Constantin, A.1    Escher, J.2
  • 8
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • _, Wave breaking for nonlinear nonlocal shallow water equations, Acta Math. 181 (1998), no. 2, 229-243.
    • (1998) Acta Math. , vol.181 , Issue.2 , pp. 229-243
  • 9
    • 0042279206 scopus 로고    scopus 로고
    • On the geometric approach to the motion of inertial mechanical systems
    • A. Constantin and B. Kolev, On the geometric approach to the motion of inertial mechanical systems, J. Phys. A 35 (2002), no. 32, R51-R79.
    • (2002) J. Phys. A , vol.35 , Issue.32
    • Constantin, A.1    Kolev, B.2
  • 10
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • _, Geodesic flow on the diffeomorphism group of the circle, Comment. Math. Helv. 78 (2003), no. 4, 787-804.
    • (2003) Comment. Math. Helv. , vol.78 , Issue.4 , pp. 787-804
  • 11
    • 0033415933 scopus 로고    scopus 로고
    • A shallow water equation on the circle
    • A. Constantin and H. McKean, A shallow water equation on the circle, Comm. Pure Appl. Math. 52 (1999), no. 8, 949-982.
    • (1999) Comm. Pure Appl. Math. , vol.52 , Issue.8 , pp. 949-982
    • Constantin, A.1    McKean, H.2
  • 13
    • 0000380413 scopus 로고    scopus 로고
    • Stability of the Camassa-Holm solitons
    • _, Stability of the Camassa-Holm solitons, J. Nonlinear Sci. 12 (2002), no. 4, 415-422.
    • (2002) J. Nonlinear Sci. , vol.12 , Issue.4 , pp. 415-422
  • 14
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
    • H. Dai, Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod, Acta Mech. 127 (1998), no. 1-4, 193-207.
    • (1998) Acta Mech. , vol.127 , Issue.1-4 , pp. 193-207
    • Dai, H.1
  • 16
    • 0001500560 scopus 로고    scopus 로고
    • The Camassa Holm equation: Conserved quantities and the initial value problem
    • M. Fisher and J. Schiff, The Camassa Holm equation: conserved quantities and the initial value problem, Phys. Lett. A 259 (1999), no. 5, 371-376.
    • (1999) Phys. Lett. A , vol.259 , Issue.5 , pp. 371-376
    • Fisher, M.1    Schiff, J.2
  • 18
    • 22244482803 scopus 로고    scopus 로고
    • Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
    • B. Fuchssteiner, Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa-Holm equation, Phys. D 95 (1996), no. 3-4, 229-243.
    • (1996) Phys. D , vol.95 , Issue.3-4 , pp. 229-243
    • Fuchssteiner, B.1
  • 19
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • B. Fuchssteiner and A. Fokas, Symplectic structures, their Bäcklund transformations and hereditary symmetries, Phys. D 4 (1981), no. 1, 47-66.
    • (1981) Phys. D , vol.4 , Issue.1 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.2
  • 20
    • 0038584929 scopus 로고    scopus 로고
    • Algebra-geometric solutions of the Camassa-Holm hierarchy
    • F. Gesztesy and H. Holden, Algebra-geometric solutions of the Camassa-Holm hierarchy, Rev. Mat. Iberoamericana 19 (2003), no. 1, 73-142.
    • (2003) Rev. Mat. Iberoamericana , vol.19 , Issue.1 , pp. 73-142
    • Gesztesy, F.1    Holden, H.2
  • 21
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry. I
    • M. Grillakis, J. Shatah, and W. Strauss, Stability theory of solitary waves in the presence of symmetry. I, J. Funct. Anal. 74 (1987), no. 1, 160-197.
    • (1987) J. Funct. Anal. , vol.74 , Issue.1 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 22
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, Korteweg-de Vries and related models for water waves
    • R. Johnson, Camassa-Holm, Korteweg-de Vries and related models for water waves, J. Fluid Mech. 455 (2002), 63-82.
    • (2002) J. Fluid Mech. , vol.455 , pp. 63-82
    • Johnson, R.1
  • 23
    • 1342300742 scopus 로고    scopus 로고
    • On solutions of the Camassa-Holm equation
    • _, On solutions of the Camassa-Holm equation, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 459 (2003), no. 2035, 1687-1708.
    • (2003) R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. , vol.459 , Issue.2035 , pp. 1687-1708
  • 24
    • 0037612018 scopus 로고    scopus 로고
    • Euler equations on homogeneous spaces and Virasoro orbits
    • B. Khesin and G. Misiołek, Euler equations on homogeneous spaces and Virasoro orbits, Adv. Math. 176 (2003), no. 1, 116-144.
    • (2003) Adv. Math. , vol.176 , Issue.1 , pp. 116-144
    • Khesin, B.1    Misiołek, G.2
  • 25
    • 0036434830 scopus 로고    scopus 로고
    • The scattering approach for the Camassa-Holm equation
    • J. Lenells, The scattering approach for the Camassa-Holm equation, J. Nonlinear Math. Phys. 9 (2002), no. 4, 389-393.
    • (2002) J. Nonlinear Math. Phys. , vol.9 , Issue.4 , pp. 389-393
    • Lenells, J.1
  • 26
    • 1342267624 scopus 로고    scopus 로고
    • Stability of periodic peakons
    • _, Stability of periodic peakons, Int. Math. Res. Not. 2004 (2004), no. 10, 485-499.
    • (2004) Int. Math. Res. Not. , vol.2004 , Issue.10 , pp. 485-499
  • 27
    • 2442664231 scopus 로고    scopus 로고
    • A variational approach to the stability of periodic peakons
    • _, A variational approach to the stability of periodic peakons, J. Nonlinear Math. Phys. 11 (2004), no. 2, 151-163.
    • (2004) J. Nonlinear Math. Phys. , vol.11 , Issue.2 , pp. 151-163
  • 30
    • 10044227192 scopus 로고    scopus 로고
    • Traveling wave solutions of the Camassa-Holm and Korteweg-de fries equations
    • _, Traveling wave solutions of the Camassa-Holm and Korteweg-de fries equations, J. Nonlinear Math. Phys. 11 (2004), 508-520.
    • (2004) J. Nonlinear Math. Phys. , vol.11 , pp. 508-520
  • 31
    • 0002497535 scopus 로고
    • Integrable systems and algebraic curves
    • Global Analysis (Proc. Biennial Sem. Canad. Math. Congr., Univ. Calgary, Calgary, Alberta, 1978), Springer, Berlin
    • H. McKean, Integrable systems and algebraic curves, Global Analysis (Proc. Biennial Sem. Canad. Math. Congr., Univ. Calgary, Calgary, Alberta, 1978), Lecture Notes in Math., vol. 755, Springer, Berlin, 1979, pp. 83-200.
    • (1979) Lecture Notes in Math. , vol.755 , pp. 83-200
    • McKean, H.1
  • 32
    • 0001253693 scopus 로고
    • The spectrum of Hill's equation
    • H. McKean and P. van Moerbeke, The spectrum of Hill's equation, Invent. Math. 30 (1975), no. 3, 217-274.
    • (1975) Invent. Math. , vol.30 , Issue.3 , pp. 217-274
    • McKean, H.1    Van Moerbeke, P.2
  • 33
    • 0031989845 scopus 로고    scopus 로고
    • A shallow water equation as a geodesic flow on the Bott-Virasoro group
    • G. Misiołek, A shallow water equation as a geodesic flow on the Bott-Virasoro group, J. Geom. Phys. 24 (1998), no. 3, 203-208.
    • (1998) J. Geom. Phys. , vol.24 , Issue.3 , pp. 203-208
    • Misiołek, G.1
  • 34
    • 0003317858 scopus 로고
    • Applications of lie groups to differential equations, 2nd ed
    • Springer, New York
    • P. Olver, Applications of Lie Groups to Differential Equations, 2nd ed., Graduate Texts in Mathematics, vol. 107, Springer, New York, 1993.
    • (1993) Graduate Texts in Mathematics , vol.107
    • Olver, P.1
  • 35
    • 34250093431 scopus 로고
    • The super Korteweg-de Vries equation as an Euler equation
    • V. Ovsienko and B. Khesin, The super Korteweg-de Vries equation as an Euler equation, Funktsional. Anal. i Prilozhen. 21 (1987), no. 4, 81-82.
    • (1987) Funktsional. Anal. I Prilozhen , vol.21 , Issue.4 , pp. 81-82
    • Ovsienko, V.1    Khesin, B.2
  • 36
    • 0038108218 scopus 로고    scopus 로고
    • Geometric integrability of the Camassa-Holm equation
    • E. Reyes, Geometric integrability of the Camassa-Holm equation, Lett. Math. Phys. 59 (2002), no. 2, 117-131.
    • (2002) Lett. Math. Phys. , vol.59 , Issue.2 , pp. 117-131
    • Reyes, E.1
  • 37
    • 0030544208 scopus 로고    scopus 로고
    • Zero curvature formulations of dual hierarchies
    • J. Schiff, Zero curvature formulations of dual hierarchies, J. Math. Phys. 37 (1996), no. 4, 1928-1938.
    • (1996) J. Math. Phys. , vol.37 , Issue.4 , pp. 1928-1938
    • Schiff, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.