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Volumn 33, Issue 1-2, 2003, Pages 73-95

Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves

Author keywords

[No Author keywords available]

Indexed keywords

INTEGRAL EQUATIONS; SURFACE TENSION; WAVE EQUATIONS;

EID: 0038170210     PISSN: 01695983     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0169-5983(03)00046-7     Document Type: Article
Times cited : (267)

References (38)
  • 1
    • 0000310316 scopus 로고
    • The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
    • Alber M. Camassa R. Holm D.D. Marsden J.E. The geometry of peaked solitons and billiard solutions of a class of integrable PDE's Lett. Math. Phys. 32 1994 137-151
    • (1994) Lett. Math. Phys. , vol.32 , pp. 137-151
    • Alber, M.1    Camassa, R.2    Holm, D.D.3    Marsden, J.E.4
  • 3
    • 0035641135 scopus 로고    scopus 로고
    • The complex geometry of weak piecewise smooth solutions of integrable non-linear PDE's of shallow water and Dym type
    • Alber M. Camassa R. Fedorov V.N. Holm D.D. Marsden J.E. The complex geometry of weak piecewise smooth solutions of integrable non-linear PDE's of shallow water and Dym type Commun. Math. Phys. 221 2001 197-227
    • (2001) Commun. Math. Phys. , vol.221 , pp. 197-227
    • Alber, M.1    Camassa, R.2    Fedorov, V.N.3    Holm, D.D.4    Marsden, J.E.5
  • 4
    • 84990623719 scopus 로고
    • Solitary water waves with capillary ripples at infinity
    • Beale T.J. Solitary water waves with capillary ripples at infinity Commun. Pure Appl. Math. 64 1991 211-257
    • (1991) Commun. Pure Appl. Math. , vol.64 , pp. 211-257
    • Beale, T.J.1
  • 5
    • 0001077774 scopus 로고
    • The solitary wave with surface tension
    • Benjamin T.B. The solitary wave with surface tension Quart. Appl. Math. 40 1982 231-234
    • (1982) Quart. Appl. Math. , vol.40 , pp. 231-234
    • Benjamin, T.B.1
  • 6
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • Camassa R. Holm D.D. 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
  • 7
    • 0037051411 scopus 로고    scopus 로고
    • Do true elevation solitary waves exist? A numerical investigation
    • Champneys A.R. Vanden-Broek J.-M. Lord G.J. Do true elevation solitary waves exist? A numerical investigation J. Fluid Mech. 454 2002 403-417
    • (2002) J. Fluid Mech. , vol.454 , pp. 403-417
    • Champneys, A.R.1    Vanden-Broek, J.-M.2    Lord, G.J.3
  • 8
    • 0002053850 scopus 로고    scopus 로고
    • Asymptotic integrability
    • A. Degasperis, & G. Gaeta (Eds.), Singapore: World Scientific
    • Degasperis A. Procesi M. Asymptotic integrability Degasperis A. Gaeta G. Symmetry and Perturbation Theory 1999 23-37 World Scientific Singapore
    • (1999) Symmetry and Perturbation Theory , pp. 23-37
    • Degasperis, A.1    Procesi, M.2
  • 10
    • 0033489572 scopus 로고    scopus 로고
    • Nonlinear gravity and capillary-gravity waves
    • Dias F. Kharif C. Nonlinear gravity and capillary-gravity waves Ann. Rev. Fluid Mech. 31 1999 301-346
    • (1999) Ann. Rev. Fluid Mech. , vol.31 , pp. 301-346
    • Dias, F.1    Kharif, C.2
  • 11
    • 40749103220 scopus 로고    scopus 로고
    • An integrable shallow water equation with linear and non-linear dispersion
    • Dullin H.R. Gottwald G. Holm D.D. An integrable shallow water equation with linear and non-linear dispersion Phys. Rev. Lett. 87 2001 4501-4504
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 4501-4504
    • Dullin, H.R.1    Gottwald, G.2    Holm, D.D.3
  • 12
    • 0002630451 scopus 로고
    • Bäcklund transformations for hereditary symmetries
    • Fokas A.S. Fuchssteiner B. Bäcklund transformations for hereditary symmetries Nonlinear Anal. TMA 5 1981 423-432
    • (1981) Nonlinear Anal. TMA , vol.5 , pp. 423-432
    • Fokas, A.S.1    Fuchssteiner, B.2
  • 13
    • 4243241002 scopus 로고    scopus 로고
    • Asymptotic integrability of water waves
    • Fokas A.S. Liu Q.M. Asymptotic integrability of water waves Phys. Rev. Lett. 77 1996 2347-2351
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 2347-2351
    • Fokas, A.S.1    Liu, Q.M.2
  • 14
    • 22244482803 scopus 로고    scopus 로고
    • Some tricks from the symmetry-toolbox for non-linear equations: Generalization of the Camassa-Holm equation
    • Fuchssteiner B. Some tricks from the symmetry-toolbox for non-linear equations: generalization of the Camassa-Holm equation Physica D 95 1996 229-243
    • (1996) Physica D , vol.95 , pp. 229-243
    • Fuchssteiner, B.1
  • 15
    • 85068161709 scopus 로고
    • Weakly nonlocal solitary waves in a singularly perturbed Korteweg-de-Vries equation textit
    • Grimshaw R.H.J. Joshi N. Weakly nonlocal solitary waves in a singularly perturbed Korteweg-de-Vries equation textit SIAM J. Appl. Math. 55 1995 124-135
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 124-135
    • Grimshaw, R.H.J.1    Joshi, N.2
  • 16
    • 45849155444 scopus 로고    scopus 로고
    • Cuspons and regular gap solitons between three dispersion curves
    • Grimshaw R.H.J. Malomed B. Gottwald G.A. Cuspons and regular gap solitons between three dispersion curves Phys. Rev. E 65 2002 6606-6620
    • (2002) Phys. Rev. E , vol.65 , pp. 6606-6620
    • Grimshaw, R.H.J.1    Malomed, B.2    Gottwald, G.A.3
  • 17
    • 0037429710 scopus 로고    scopus 로고
    • Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary PDEs
    • Holm D.D. Staley M.F. Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary PDEs Phys. Lett. A 308 2003 2003
    • (2003) Phys. Lett. A , vol.308 , pp. 2003
    • Holm, D.D.1    Staley, M.F.2
  • 18
    • 1142303186 scopus 로고    scopus 로고
    • Wave structures and nonlinear balances in a family of evolutionary PDEs
    • Systems, to appear
    • Holm, D.D., Staley, M.F., 2003b. Wave structures and nonlinear balances in a family of evolutionary PDEs. SIAM J. Dyn. Systems, 2003, to appear.
    • (2003) SIAM J. Dyn.
    • Holm, D.D.1    Staley, M.F.2
  • 19
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, Korteweg-de Vries and related models for water waves
    • Johnson R.S. 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
  • 20
    • 0030677019 scopus 로고    scopus 로고
    • Nonlinear, dispersive long waves in water of variable depth
    • Hunt, J.N. (Ed.), Gravity Waves on Water of Variable Depth. Computational Mechanics Publications, Billerica, MA
    • Kirby, J.T., 1997. Nonlinear, dispersive long waves in water of variable depth. Adv. Fluid Mech. 10, 55-125; In: Hunt, J.N. (Ed.), Gravity Waves on Water of Variable Depth. Computational Mechanics Publications, Billerica, MA.
    • (1997) Adv. Fluid Mech. , vol.10 , pp. 55-125
    • Kirby, J.T.1
  • 21
    • 19044397263 scopus 로고
    • On integrable systems with higher order corrections
    • Kodama Y. On integrable systems with higher order corrections Phys. Lett. A 107 1985 245-249
    • (1985) Phys. Lett. A , vol.107 , pp. 245-249
    • Kodama, Y.1
  • 22
    • 0000156026 scopus 로고
    • Normal forms for weakly dispersive wave equations
    • Kodama Y. Normal forms for weakly dispersive wave equations Phys. Lett. A 112 1985 193-196
    • (1985) Phys. Lett. A , vol.112 , pp. 193-196
    • Kodama, Y.1
  • 23
    • 0000434210 scopus 로고
    • On solitary-wave interaction
    • Kodama Y. On solitary-wave interaction Phys. Lett. A 123 1987 276-282
    • (1987) Phys. Lett. A , vol.123 , pp. 276-282
    • Kodama, Y.1
  • 24
    • 85031156747 scopus 로고    scopus 로고
    • private communication
    • Kodama, Y., 2001. private communication.
    • (2001)
    • Kodama, Y.1
  • 25
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular channel, and a new type of long stationary waves
    • Korteweg D.J. de Vries G. On the change of form of long waves advancing in a rectangular channel, and a new type of long stationary waves Philos. Mag. 39 5 1895 422-443
    • (1895) Philos. Mag. , vol.39 , Issue.5 , pp. 422-443
    • Korteweg, D.J.1    de Vries, G.2
  • 26
    • 0031537418 scopus 로고    scopus 로고
    • An improved theory of long waves on the water surface
    • Li Z. Sibgatullin N.R. An improved theory of long waves on the water surface J. Appl. Math. Mech. 61 1997 177-182
    • (1997) J. Appl. Math. Mech. , vol.61 , pp. 177-182
    • Li, Z.1    Sibgatullin, N.R.2
  • 28
    • 0013098173 scopus 로고    scopus 로고
    • Oscillatory integrals and phenomena beyond all algebraic orders. With applications to homoclinic orbits in reversible systems
    • Springer, Berlin
    • Lombardi, E., 2000. Oscillatory integrals and phenomena beyond all algebraic orders. With applications to homoclinic orbits in reversible systems. Lecture Notes in Mathematics, Vol. 1741. Springer, Berlin.
    • (2000) Lecture Notes in Mathematics , vol.1741
    • Lombardi, E.1
  • 29
    • 0036662157 scopus 로고    scopus 로고
    • High-order interaction of solitary waves on shallow water
    • Marchant T.R. High-order interaction of solitary waves on shallow water Stud. Appl. Math. 109 2002 1-17
    • (2002) Stud. Appl. Math. , vol.109 , pp. 1-17
    • Marchant, T.R.1
  • 30
    • 84975745401 scopus 로고
    • The extended Korteweg-de Vries equation and the resonant flow over topography
    • Marchant T.R. Smyth N.F. The extended Korteweg-de Vries equation and the resonant flow over topography J. Fluid Mech. 221 1990 263-288
    • (1990) J. Fluid Mech. , vol.221 , pp. 263-288
    • Marchant, T.R.1    Smyth, N.F.2
  • 31
    • 0037036176 scopus 로고    scopus 로고
    • Perturbative symmetry approach
    • Mikhailov A.V. Novikov V.S. Perturbative symmetry approach J. Phys. A 35 2002 4775-4790
    • (2002) J. Phys. A , vol.35 , pp. 4775-4790
    • Mikhailov, A.V.1    Novikov, V.S.2
  • 32
    • 0000462631 scopus 로고
    • Hamiltonian perturbation theory and water waves
    • Olver P. Hamiltonian perturbation theory and water waves Contemp. Math. 28 1983 231-249
    • (1983) Contemp. Math. , vol.28 , pp. 231-249
    • Olver, P.1
  • 33
    • 84958444374 scopus 로고
    • Calculations of the development of an undular bore
    • Peregrine D.H. Calculations of the development of an undular bore J. Fluid Mech. 25 1966 321-330
    • (1966) J. Fluid Mech. , vol.25 , pp. 321-330
    • Peregrine, D.H.1
  • 34
    • 0031224876 scopus 로고    scopus 로고
    • On the generation of shelves by long non-linear waves in stratified flows
    • Prasad D. Akylas T.R. On the generation of shelves by long non-linear waves in stratified flows J. Fluid Mech. 346 1997 345-362
    • (1997) J. Fluid Mech. , vol.346 , pp. 345-362
    • Prasad, D.1    Akylas, T.R.2
  • 35
    • 0034825095 scopus 로고    scopus 로고
    • Peakons and periodic cusp waves in a generalized Camassa-Holm equation
    • Qian T. Tang M. Peakons and periodic cusp waves in a generalized Camassa-Holm equation Chaos, Solitons Fractals 12 2001 1347-1360
    • (2001) Chaos, Solitons Fractals , vol.12 , pp. 1347-1360
    • Qian, T.1    Tang, M.2
  • 36
    • 0034364719 scopus 로고    scopus 로고
    • The long wave limit for the water wave problem-I. The case of zero surface tension
    • Schneider G. Wayne C.E. The long wave limit for the water wave problem-I. The case of zero surface tension Commun. Pure Appl. Math. 53 2000 1475-1535
    • (2000) Commun. Pure Appl. Math. , vol.53 , pp. 1475-1535
    • Schneider, G.1    Wayne, C.E.2
  • 38
    • 0009792695 scopus 로고    scopus 로고
    • Nonlinear waves and solitons in water
    • Wu, Ted, 1998. Nonlinear waves and solitons in water. Physica D 123, 48-63.
    • (1998) Physica D , vol.123 , pp. 48-63
    • Wu Ted1


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