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Volumn 13, Issue 7-8, 2008, Pages 681-732

An explicit finite difference scheme for the Camassa-Holm equation

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EID: 69549112729     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (16)

References (41)
  • 1
    • 33644862175 scopus 로고    scopus 로고
    • Numerical simulation of Camassa-Holm peakons by adaptive upwinding
    • R. Artebrant and H. J. Schroll, Numerical simulation of Camassa-Holm peakons by adaptive upwinding, Appl. Numer. Math., 56 (2006), 695-711.
    • (2006) Appl. Numer. Math. , vol.56 , pp. 695-711
    • Artebrant, R.1    Schroll, H.J.2
  • 2
    • 0034714658 scopus 로고    scopus 로고
    • Multipeakons and the classical moment problem
    • R. Beals, D. H. Sattinger, and J. Szmigielski, Multipeakons and the classical moment problem, Adv. Math., 154 (2000), 229-257.
    • (2000) Adv. Math. , vol.154 , pp. 229-257
    • Beals, R.1    Sattinger, D.H.2    Szmigielski, J.3
  • 3
    • 33846878957 scopus 로고    scopus 로고
    • Global conservative solutions of the Camassa-Holm equation
    • A. Bressan and A. Constantin, Global conservative solutions of the Camassa-Holm equation, Arch. Ration. Mech. Anal., 183 (2007), 215-239.
    • (2007) Arch. Ration. Mech. Anal. , vol.183 , pp. 215-239
    • Bressan, A.1    Constantin, A.2
  • 4
    • 51149109959 scopus 로고    scopus 로고
    • Global dissipative solutions of the Camassa-Holm equation
    • A. Bressan and A. Constantin, Global dissipative solutions of the Camassa-Holm equation, Anal. Appl. (Singap.), 5 (2007), 1-27.
    • (2007) Anal. Appl. (Singap. ) , vol.5 , pp. 1-27
    • Bressan, A.1    Constantin, A.2
  • 5
    • 33845317002 scopus 로고    scopus 로고
    • An optimal transportation metric for solutions of the Camassa-Holm equation
    • A. Bressan and M. Fonte, An optimal transportation metric for solutions of the Camassa-Holm equation, Methods Appl. Anal., 12 (2005), 191-219.
    • (2005) Methods Appl. Anal. , vol.12 , pp. 191-219
    • Bressan, A.1    Fonte, M.2
  • 6
    • 0041760859 scopus 로고    scopus 로고
    • Characteristics and the initial value problem of a completely integrable shallow water equation
    • R. Camassa, Characteristics and the initial value problem of a completely integrable shallow water equation, Discrete Contin. Dyn. Syst. Ser. B, 3 (2003), 115-139.
    • (2003) Discrete Contin. Dyn. Syst. Ser. B , vol.3 , pp. 115-139
    • Camassa, R.1
  • 7
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett., 71 (1993), 1661-1664.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 8
    • 56349110516 scopus 로고
    • A new integrable shallow water equation
    • R. Camassa, D. D. Holm, and J. Hyman, A new integrable shallow water equation, Adv. Appl. Mech., 31 (1994), 1-33.
    • (1994) Adv. Appl. Mech. , vol.31 , pp. 1-33
    • Camassa, R.1    Holm, D.D.2    Hyman, J.3
  • 9
    • 30444460126 scopus 로고    scopus 로고
    • On a completely integrable numerical scheme for a nonlinear shallow-water wave equation
    • R. Camassa, J. Huang, and L. Lee, On a completely integrable numerical scheme for a nonlinear shallow-water wave equation, J. Nonlinear Math. Phys., 12 (2005), 146-162.
    • (2005) J. Nonlinear Math. Phys. , vol.12 , pp. 146-162
    • Camassa, R.1    Huang, J.2    Lee, L.3
  • 10
    • 33646924886 scopus 로고    scopus 로고
    • Integral and integrable algorithms for a nonlinear shallow-water wave equation
    • R. Camassa, J. Huang, and L. Lee, Integral and integrable algorithms for a nonlinear shallow-water wave equation, J. Comput. Phys., 216 (2006), 547-572.
    • (2006) J. Comput. Phys. , vol.216 , pp. 547-572
    • Camassa, R.1    Huang, J.2    Lee, L.3
  • 11
    • 33746133952 scopus 로고    scopus 로고
    • Global weak solutions to a generalized hyperelastic-rod wave equation
    • (elec-tronic)
    • G. M. Coclite, H. Holden, and K. H. Karlsen, Global weak solutions to a generalized hyperelastic-rod wave equation, SIAM J. Math. Anal., 37 (2005), 1044-1069 (elec-tronic).
    • (2005) SIAM J. Math. Anal. , vol.37 , pp. 1044-1069
    • Coclite, G.M.1    Holden, H.2    Karlsen, K.H.3
  • 12
    • 49749109221 scopus 로고    scopus 로고
    • A convergent _nite di_erence scheme for the Camassa-Holm equation with general H1 initial data
    • G. M. Coclite, K. H. Karlsen, and N. H. Risebro, A convergent _nite di_erence scheme for the Camassa-Holm equation with general H1 initial data, SIAM J. Numer. Anal., 46 (2008), 1554|1579.
    • (2008) SIAM J. Numer. Anal. , vol.46 , pp. 1554-1579
    • Coclite, G.M.1    Karlsen, K.H.2    Risebro, N.H.3
  • 13
    • 42649132824 scopus 로고    scopus 로고
    • Multi-symplectic integration of the Camassa-Holm equation
    • D. Cohen, B. Owren, and X. Raynaud, Multi-symplectic integration of the Camassa-Holm equation, J. Comput. Phys., 227 (2008), 5492-5512.
    • (2008) J. Comput. Phys. , vol.227 , pp. 5492-5512
    • Cohen, D.1    Owren, B.2    Raynaud, X.3
  • 15
    • 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. 26 (1998), 303-328.
    • (1998) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.26 , pp. 303-328
    • Constantin, A.1    Escher, J.2
  • 16
    • 0000468550 scopus 로고    scopus 로고
    • Global weak solutions for a shallow water equation
    • A. Constantin and J. Escher, Global weak solutions for a shallow water equation, Indiana Univ. Math. J., 47 (1998), 1527-1545.
    • (1998) Indiana Univ. Math. J. , vol.47 , pp. 1527-1545
    • Constantin, A.1    Escher, J.2
  • 17
    • 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), R51-R79.
    • (2002) J. Phys. A , vol.35
    • Constantin, A.1    Kolev, B.2
  • 18
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic ow on the di_eomorphism group of the circle
    • A. Constantin and B. Kolev, Geodesic ow on the di_eomorphism group of the circle, Comment. Math. Helv., 78 (2003), 787-804.
    • (2003) Comment. Math. Helv. , vol.78 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 19
    • 0033415933 scopus 로고    scopus 로고
    • A shallow water equation on the circle
    • A. Constantin and H. P. McKean, A shallow water equation on the circle, Comm. Pure Appl. Math., 52 (1999), 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
    • A. Constantin and L. Molinet, Global weak solutions for a shallow water equation, Comm. Math. Phys., 211 (2000), 45-61.
    • (2000) Comm. Math. Phys. , vol.211 , pp. 45-61
    • Constantin, A.1    Molinet, L.2
  • 21
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible mooney-rivlin rod
    • H. H. Dai, Model equations for nonlinear dispersive waves in a compressible mooney-rivlin rod, Acta Mechanica, 127 (1998), 193-207.
    • (1998) Acta Mechanica , vol.127 , pp. 193-207
    • Dai, H.H.1
  • 22
    • 0000830886 scopus 로고    scopus 로고
    • A few remarks on the Camassa-Holm equation
    • R. Danchin, A few remarks on the Camassa-Holm equation, Di_erential Integral Equa-tions, 14 (2001), 953-988.
    • (2001) Di_erential Integral Equa-tions , vol.14 , pp. 953-988
    • Danchin, R.1
  • 23
    • 0043159153 scopus 로고    scopus 로고
    • A note on well-posedness for Camassa-Holm equation
    • R. Danchin, A note on well-posedness for Camassa-Holm equation, J. Di_erential Equations, 192 (2003), 429-444.
    • (2003) J. Di_erential Equations , vol.192 , pp. 429-444
    • Danchin, R.1
  • 24
    • 77954774514 scopus 로고    scopus 로고
    • Oxford Lecture Series in Mathematics and its Applications
    • Oxford University Press, Oxford
    • E. Feireisl, "Dynamics of Viscous Compressible Fluids," volume 26 of Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2004.
    • (2004) Dynamics of Viscous Compressible Fluids , vol.26
    • Feireisl, E.1
  • 25
    • 0035311815 scopus 로고    scopus 로고
    • Integrable vs. nonintegrable geodesic soliton behavior
    • O. B. Fringer and D. D. Holm, Integrable vs. nonintegrable geodesic soliton behavior, Phys. D, 150 (2001), 237-263.
    • (2001) Phys. D , vol.150 , pp. 237-263
    • Fringer, O.B.1    Holm, D.D.2
  • 26
    • 49049150360 scopus 로고    scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • B. Fuchssteiner and A. S. Fokas, Symplectic structures, their Bäcklund transformations and hereditary symmetries, Phys. D, 4 (1981/82), 47-66.
    • Phys. D , vol.4 , Issue.1981-1982 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 27
    • 34447276776 scopus 로고    scopus 로고
    • Convergence of a _nite di_erence scheme for the Camassa-Holm equation
    • H. Holden and X. Raynaud, Convergence of a _nite di_erence scheme for the Camassa-Holm equation, SIAM J. Num. Anal., 44 (2006), 1655|1680.
    • (2006) SIAM J. Num. Anal. , vol.44 , pp. 1655-1680
    • Holden, H.1    Raynaud, X.2
  • 28
    • 33644554516 scopus 로고    scopus 로고
    • A convergent numerical scheme for the Camassa-Holm equation based on multipeakons
    • H. Holden and X. Raynaud, A convergent numerical scheme for the Camassa-Holm equation based on multipeakons, Discrete Contin. Dyn. Syst., 14 (2006), 505-523.
    • (2006) Discrete Contin. Dyn. Syst. , vol.14 , pp. 505-523
    • Holden, H.1    Raynaud, X.2
  • 29
    • 35648988600 scopus 로고    scopus 로고
    • Global conservative solutions of the Camassa-Holm equation - a Lagrangian point of view
    • H. Holden and X. Raynaud, Global conservative solutions of the Camassa-Holm equation - a Lagrangian point of view, Comm. Partial Di_erential Equations, 32 (2007), 1511-1549.
    • (2007) Comm. Partial Di_erential Equations , vol.32 , pp. 1511-1549
    • Holden, H.1    Raynaud, X.2
  • 30
    • 0001971504 scopus 로고    scopus 로고
    • The Euler-Poincar_e equations and semidirect products with applications to continuum theories
    • D. D. Holm, J. E. Marsden, and T. S. Ratiu, The Euler-Poincar_e equations and semidirect products with applications to continuum theories, Adv. Math., 137 (1998), 1-81.
    • (1998) Adv. Math. , vol.137 , pp. 1-81
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3
  • 31
    • 1142303186 scopus 로고    scopus 로고
    • Wave structure and nonlinear balances in a family of evolutionary PDEs
    • (electronic)
    • D. D. Holm and M. F. Staley, Wave structure and nonlinear balances in a family of evolutionary PDEs, SIAM J. Appl. Dyn. Syst., 2 (2003), 323-380 (electronic).
    • (2003) SIAM J. Appl. Dyn. Syst. , vol.2 , pp. 323-380
    • Holm, D.D.1    Staley, M.F.2
  • 32
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, Korteweg-de Vries and related models for water waves
    • R. S. 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.S.1
  • 33
    • 33748553654 scopus 로고    scopus 로고
    • Convergence of a spectral projection of the Camassa-Holm equation
    • H. Kalisch and X. Raynaud, Convergence of a spectral projection of the Camassa-Holm equation, Numer. Methods Partial Di_erential Equations, 22 (2006), 1197-1215.
    • (2006) Numer. Methods Partial Di_erential Equations , vol.22 , pp. 1197-1215
    • Kalisch, H.1    Raynaud, X.2
  • 34
    • 0034688728 scopus 로고    scopus 로고
    • Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
    • Y. A. Li and P. J. Olver, Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation, J. Di_erential Equations, 162 (2000), 27-63.
    • (2000) J. Di_erential Equations , vol.162 , pp. 27-63
    • Li, Y.A.1    Olver, P.J.2
  • 35
    • 84867945317 scopus 로고    scopus 로고
    • Formation and dynamics of shock waves in the Degasperis-Procesi equation
    • H. Lundmark, Formation and dynamics of shock waves in the Degasperis-Procesi equation, J. Nonlinear Sci., 17 (2007), 169-198.
    • (2007) J. Nonlinear Sci. , vol.17 , pp. 169-198
    • Lundmark, H.1
  • 36
    • 0031989845 scopus 로고    scopus 로고
    • A shallow water equation as a geodesic ow on the Bott-Virasoro group
    • G. Misiolek, A shallow water equation as a geodesic ow on the Bott-Virasoro group, J. Geom. Phys., 24 (1998), 203-208.
    • (1998) J. Geom. Phys. , vol.24 , pp. 203-208
    • Misiolek, G.1
  • 37
    • 0035479874 scopus 로고    scopus 로고
    • On the Cauchy problem for the Camassa-Holm equation, Non-linear Anal., 46 (Ser. A: Theory Methods)
    • G. Rodríguez-Blanco, On the Cauchy problem for the Camassa-Holm equation, Non-linear Anal., 46 (Ser. A: Theory Methods) (2001), 309-327.
    • (2001) , pp. 309-327
    • Rodríguez-Blanco, G.1
  • 38
    • 0003462525 scopus 로고
    • Shock Waves and Reaction-Di_usion Equations
    • Springer-Verlag, New York, sec-ond edition
    • J. Smoller, "Shock Waves and Reaction-Di_usion Equations," volume 258 of Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, New York, sec-ond edition, 1994.
    • (1994) Grundlehren der Mathematischen Wissenschaften , vol.258
    • Smoller, J.1
  • 39
    • 0034394008 scopus 로고    scopus 로고
    • On the weak solutions to a shallow water equation
    • Z. Xin and P. Zhang, On the weak solutions to a shallow water equation, Comm. Pure Appl. Math., 53 (2000), 1411-1433.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1411-1433
    • Xin, Z.1    Zhang, P.2
  • 40
    • 0036913863 scopus 로고    scopus 로고
    • On the uniqueness and large time behavior of the weak solutions to a shallow water equation
    • Z. Xin and P. Zhang, On the uniqueness and large time behavior of the weak solutions to a shallow water equation, Comm. Partial Di_erential Equations, 27 (2002), 1815-1844.
    • (2002) Comm. Partial Di_erential Equations , vol.27 , pp. 1815-1844
    • Xin, Z.1    Zhang, P.2
  • 41
    • 55349125734 scopus 로고    scopus 로고
    • A local discontinuous Galerkin method for the Camassa-Holm equation
    • Y. Xu and C.-W. Shu, A local discontinuous Galerkin method for the Camassa-Holm equation, Siam J. Numer. Anal., 43 (2008), 1998-2021.
    • (2008) Siam J. Numer. Anal. , vol.43 , pp. 1998-2021
    • Xu, Y.1    Shu, C.-W.2


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