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Volumn 11, Issue 4, 2004, Pages 508-520

Traveling wave solutions of the camassa-holm and korteweg-de vries equations

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EID: 10044227192     PISSN: 14029251     EISSN: 17760852     Source Type: Journal    
DOI: 10.2991/jnmp.2004.11.4.7     Document Type: Article
Times cited : (31)

References (45)
  • 2
    • 0000174121 scopus 로고    scopus 로고
    • Acoustic scattering and the extended Korteweg-de Vries hierarchy
    • Beals, R, Sattinger, D, and Szmigielski, J. 1998. Acoustic scattering and the extended Korteweg-de Vries hierarchy. Adv. Math., 40:190–206.
    • (1998) Adv. Math. , vol.40 , pp. 190-206
    • Beals, R.1    Sattinger, D.2    Szmigielski, J.3
  • 3
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • Camassa, R, and Holm, 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.2
  • 4
    • 56349110516 scopus 로고
    • A new integrable shallow water equation
    • Camassa, R, Holm, D, and Hyman, J. 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.2    Hyman, J.3
  • 6
    • 0000213450 scopus 로고    scopus 로고
    • On the Cauchy problem for the periodic Camassa-Holm equation
    • Constantin, A. 1997. On the Cauchy problem for the periodic Camassa-Holm equation. J. Differen-tial Equations, 141:218–235.
    • (1997) J. Differen-tial Equations , vol.141 , pp. 218-235
    • Constantin, A.1
  • 7
    • 0000684999 scopus 로고    scopus 로고
    • On the inverse spectral problem for the Camassa-Holm equation
    • Constantin, A. 1998. On the inverse spectral problem for the Camassa-Holm equation. J. Funct. Anal., 155:352–363.
    • (1998) J. Funct. Anal. , vol.155 , pp. 352-363
    • Constantin, A.1
  • 8
    • 0034415062 scopus 로고    scopus 로고
    • Existence of permanent and breaking waves for a shallow water equation: A geometric approach
    • Constantin, A. 2000. Existence of permanent and breaking waves for a shallow water equation:a geometric approach. Ann. Inst. Fourier (Grenoble), 50:321–362.
    • (2000) Ann. Inst. Fourier (Grenoble) , vol.50 , pp. 321-362
    • Constantin, A.1
  • 9
    • 34447130573 scopus 로고    scopus 로고
    • On the scattering problem for the Camassa-Holm equation
    • Constantin, A. 2001. On the scattering problem for the Camassa-Holm equation. Proc. Roy. Soc. London, 457:953–970.
    • (2001) Proc. Roy. Soc. London , vol.457 , pp. 953-970
    • Constantin, A.1
  • 10
    • 0035480042 scopus 로고    scopus 로고
    • A Lagrangian approximation to the water-wave problem
    • Constantin, A. 2001. A Lagrangian approximation to the water-wave problem. Applied Mathematics Letters, 14:789–795.
    • (2001) Applied Mathematics Letters , vol.14 , pp. 789-795
    • Constantin, A.1
  • 11
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • Constantin, A, and Escher, J. 1998. Wave breaking for nonlinear nonlocal shallow water equations. Acta Mathematica, 181:229–243.
    • (1998) Acta Mathematica , vol.181 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 12
    • 85129402022 scopus 로고    scopus 로고
    • Global existence and blow-up for a shallow water equation
    • Constantin, A, and Escher, J. 1998. Global existence and blow-up for a shallow water equation. Annali Sc. Norm. Sup. Pisa, 26:303–328.
    • (1998) Annali Sc. Norm. Sup. Pisa , vol.26 , pp. 303-328
    • Constantin, A.1    Escher, J.2
  • 13
    • 0032374820 scopus 로고    scopus 로고
    • Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
    • Constantin, A, and Escher, J. 1998. Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation. Comm. Pure Appl. Math, 51:475–504.
    • (1998) Comm. Pure Appl. Math , vol.51 , pp. 475-504
    • Constantin, A.1    Escher, J.2
  • 14
    • 0034347295 scopus 로고    scopus 로고
    • On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
    • Constantin, A, and Escher, J. 2000. On the blow-up rate and the blow-up set of breaking waves for a shallow water equation. Math. Z., 233:75–91.
    • (2000) Math. Z. , vol.233 , pp. 75-91
    • Constantin, A.1    Escher, J.2
  • 15
    • 0000468550 scopus 로고    scopus 로고
    • Global weak solutions for a shallow water equation
    • Constantin, A, and Escher, J. 1998. Global weak solutions for a shallow water equation. Indiana Univ. Math. J., 47:1527–1545.
    • (1998) Indiana Univ. Math. J. , vol.47 , pp. 1527-1545
    • Constantin, A.1    Escher, J.2
  • 16
    • 0042279206 scopus 로고    scopus 로고
    • On the geometric approach to the motion of inertial mechanical systems
    • Constantin, A, and Kolev, B. 2002. On the geometric approach to the motion of inertial mechanical systems. J. Phys. A, 35:R51–R79.
    • (2002) J. Phys. A , vol.35 , pp. R51-R79
    • Constantin, A.1    Kolev, B.2
  • 17
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • Constantin, A, and Kolev, B. 2003. Geodesic flow on the diffeomorphism group of the circle. Comment. Math. Helv., 78:787–804.
    • (2003) Comment. Math. Helv. , vol.78 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 18
    • 0042023771 scopus 로고    scopus 로고
    • On the inverse scattering approach to the Camassa-Holm equation
    • Constantin, A, and Lenells, J. 2003. On the inverse scattering approach to the Camassa-Holm equation. J. Nonlinear Math. Phys., 10:252–255.
    • (2003) J. Nonlinear Math. Phys. , vol.10 , pp. 252-255
    • Constantin, A.1    Lenells, J.2
  • 19
    • 0033415933 scopus 로고    scopus 로고
    • A shallow water equation on the circle
    • Constantin, A, and McKean, HP. 1999. A shallow water equation on the circle. Comm. Pure Appl. Math., 52:949–982.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 949-982
    • Constantin, A.1    McKean, H.P.2
  • 20
    • 0034349440 scopus 로고    scopus 로고
    • Global weak solutions for a shallow water equation
    • Constantin, A, and Molinet, L. 2000. Global weak solutions for a shallow water equation. Comm. Math. Phys., 211:45–61.
    • (2000) Comm. Math. Phys. , vol.211 , pp. 45-61
    • Constantin, A.1    Molinet, L.2
  • 22
    • 0000380413 scopus 로고    scopus 로고
    • Stability of the Camassa-Holm solitons
    • Constantin, A, and Strauss, W. 2002. Stability of the Camassa-Holm solitons. J. Nonlinear Sci., 12:415–422.
    • (2002) J. Nonlinear Sci. , vol.12 , pp. 415-422
    • Constantin, A.1    Strauss, W.2
  • 23
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
    • Dai, HH. 1998. Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. Acta Mech., 127:193–207.
    • (1998) Acta Mech. , vol.127 , pp. 193-207
    • Dai, H.H.1
  • 24
    • 0000830886 scopus 로고    scopus 로고
    • A few remarks on the Camassa-Holm equation
    • Danchin, R. 2001. A few remarks on the Camassa-Holm equation. Differential Integral Equations, 14:953–988.
    • (2001) Differential Integral Equations , vol.14 , pp. 953-988
    • Danchin, R.1
  • 26
    • 40749103220 scopus 로고    scopus 로고
    • An integrable shallow water equation with linear and nonlinear dispersion
    • Dullin, HR, Gottwald, G, and Holm, DD. 2001. An integrable shallow water equation with linear and nonlinear dispersion. Phys. Rev. Lett., 87:194501–04.
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 194501-194504
    • Dullin, H.R.1    Gottwald, G.2    Holm, D.D.3
  • 27
    • 0038170210 scopus 로고    scopus 로고
    • Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves
    • Dullin, HR, Gottwald, G, Holm, DD, and Camassa-Holm. 2003. Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves. Fluid Dyn. Res., 33:73–95.
    • (2003) Fluid Dyn. Res. , vol.33 , pp. 73-95
    • Dullin, H.R.1    Gottwald, G.2    Holm, D.D.3    Camassa-Holm4
  • 28
    • 0001702502 scopus 로고
    • On a class of physically important integrable equations
    • Fokas, AS. 1995. On a class of physically important integrable equations. Physica D, 87:145–150.
    • (1995) Physica D , vol.87 , pp. 145-150
    • Fokas, A.S.1
  • 29
    • 22244482803 scopus 로고    scopus 로고
    • Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
    • Fuchssteiner, B. 1996. Some tricks from the symmetry-toolbox for nonlinear equations:generalizations of the Camassa-Holm equation. Physica D, 95:229–243.
    • (1996) Physica D , vol.95 , pp. 229-243
    • Fuchssteiner, B.1
  • 30
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformation and hereditary symmetries
    • Fuchssteiner, B, and Fokas, AS. 1981. Symplectic structures, their Bäcklund transformation and hereditary symmetries. Physica D, 4:47–66.
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 31
    • 0038584929 scopus 로고    scopus 로고
    • Algebro-geometric solutions of the Camassa-Holm hierarchy
    • Gesztesy, F, and Holden, H. 2003. Algebro-geometric solutions of the Camassa-Holm hierarchy. Rev. Mat. Iberoamericana, 19:73–142.
    • (2003) Rev. Mat. Iberoamericana , vol.19 , pp. 73-142
    • Gesztesy, F.1    Holden, H.2
  • 32
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincaré equations and semidirect products with applications to continuum theories
    • Holm, D, Marsden, J, and Ratiu, T. 1998. The Euler-Poincaré equations and semidirect products with applications to continuum theories. Adv. Math., 137:1–81.
    • (1998) Adv. Math. , vol.137 , pp. 1-81
    • Holm, D.1    Marsden, J.2    Ratiu, T.3
  • 33
    • 0037171407 scopus 로고    scopus 로고
    • Korteweg-de Vries and related models for water waves
    • Johnson, RS, and Camassa-Holm. 2002. Korteweg-de Vries and related models for water waves. J. Fluid Mech., 455:63–82.
    • (2002) J. Fluid Mech. , vol.455 , pp. 63-82
    • Johnson, R.S.1    Camassa-Holm2
  • 34
    • 1342300742 scopus 로고    scopus 로고
    • On solutions of the Camassa-Holm equation
    • Johnson, RS. 2003. On solutions of the Camassa-Holm equation. Proc. Roy. Soc. London A, 459:1687–1708.
    • (2003) Proc. Roy. Soc. London A , vol.459 , pp. 1687-1708
    • Johnson, R.S.1
  • 35
    • 0038455796 scopus 로고    scopus 로고
    • The classical problem of water waves: A reservoir of integrable and nearlyintegrable equations
    • Johnson, RS. 2003. The classical problem of water waves:a reservoir of integrable and nearlyintegrable equations. J. Nonlinear Math. Phys., 10 (1):72–92.
    • (2003) J. Nonlinear Math. Phys. , vol.10 , Issue.1 , pp. 72-92
    • Johnson, R.S.1
  • 36
    • 0036434830 scopus 로고    scopus 로고
    • The scattering approach for the Camassa-Holm equation
    • Lenells, J. 2002. The scattering approach for the Camassa-Holm equation. J. Nonlinear Math. Phys., 9:389–393.
    • (2002) J. Nonlinear Math. Phys. , vol.9 , pp. 389-393
    • Lenells, J.1
  • 37
    • 1342267624 scopus 로고    scopus 로고
    • Stability of periodic peakons
    • Lenells, J. 2004. Stability of periodic peakons. Internat. Math. Res. Notices, 10:485–499.
    • (2004) Internat. Math. Res. Notices , vol.10 , pp. 485-499
    • Lenells, J.1
  • 38
    • 85024535231 scopus 로고    scopus 로고
    • Traveling wave solutions of the Camassa-Holm equation, submitted
    • Lenells J, Traveling wave solutions of the Camassa-Holm equation, submitted.
    • Lenells, J.1
  • 39
    • 0034688728 scopus 로고    scopus 로고
    • Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
    • Li, Y, and Olver, P. 2000. Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. J. Diff. Eq., 162:27–63.
    • (2000) J. Diff. Eq. , vol.162 , pp. 27-63
    • Li, Y.1    Olver, P.2
  • 40
    • 0031989845 scopus 로고    scopus 로고
    • A shallow water equation as a geodesic flow on the Bott-Virasoro group
    • Misiolek, G. 1998. A shallow water equation as a geodesic flow on the Bott-Virasoro group. J. Geom. Phys., 24:203–208.
    • (1998) J. Geom. Phys. , vol.24 , pp. 203-208
    • Misiolek, G.1
  • 42
    • 0001472433 scopus 로고    scopus 로고
    • Breakdown of a shallow water equation
    • McKean, HP. 1998. Breakdown of a shallow water equation. Asian J. Math, 2:867–874.
    • (1998) Asian J. Math , vol.2 , pp. 867-874
    • McKean, H.P.1
  • 43
    • 0035479874 scopus 로고    scopus 로고
    • On the Cauchy problem for the Camassa-Holm equation
    • Rodriguez-Blanco, G. 2001. On the Cauchy problem for the Camassa-Holm equation. Nonl. Anal., 46:309–327.
    • (2001) Nonl. Anal. , vol.46 , pp. 309-327
    • Rodriguez-Blanco, G.1
  • 44
    • 0034394008 scopus 로고    scopus 로고
    • On the weak solutions to a shallow water equation
    • Xin, Z, and Zhang, P. 2000. On the weak solutions to a shallow water equation. Comm. Pure Appl. Math., 53:1411–1433.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1411-1433
    • Xin, Z.1    Zhang, P.2
  • 45
    • 10044224963 scopus 로고    scopus 로고
    • On the blow-up of solutions of the periodic Camassa-Holm equation
    • to appear
    • Yin, Z. On the blow-up of solutions of the periodic Camassa-Holm equation. Dyn. Cont. Disc. Imp. Syst., to appear.
    • Dyn. Cont. Disc. Imp. Syst.
    • Yin, Z.1


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