메뉴 건너뛰기




Volumn 269, Issue 3-4, 2011, Pages 1137-1153

The Degasperis-Procesi equation as a non-metric Euler equation

Author keywords

Degasperis Procesi equation; Diffeomorphisms group of the circle; Euler equation

Indexed keywords


EID: 81555201634     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-010-0778-2     Document Type: Article
Times cited : (68)

References (34)
  • 1
    • 0001356905 scopus 로고
    • Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits
    • (no. fasc. 1)
    • Arnold, V. I.: Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16(no. fasc. 1), 319-361 (1966).
    • (1966) Ann. Inst. Fourier (Grenoble) , vol.16 , pp. 319-361
    • Arnold, V.I.1
  • 3
    • 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(11), 1661-1664 (1993).
    • (1993) Phys. Rev. Lett. , vol.71 , Issue.11 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 4
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • Constantin A., Escher J.: Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 181(2), 229-243 (1998).
    • (1998) Acta Math. , vol.181 , Issue.2 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 5
    • 0032374820 scopus 로고    scopus 로고
    • Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
    • Constantin A., Escher J.: Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation. Comm. Pure Appl. Math. 51(5), 475-504 (1998).
    • (1998) Comm. Pure Appl. Math. , vol.51 , Issue.5 , pp. 475-504
    • Constantin, A.1    Escher, J.2
  • 6
    • 33846053142 scopus 로고    scopus 로고
    • Inverse scattering transform for the Camassa-Holm equation
    • Constantin A., Gerdjikov V. S., Ivanov R. I.: Inverse scattering transform for the Camassa-Holm equation. Inverse Problems 22(6), 2197-2207 (2006).
    • (2006) Inverse Problems , vol.22 , Issue.6 , pp. 2197-2207
    • Constantin, A.1    Gerdjikov, V.S.2    Ivanov, R.I.3
  • 7
    • 0042279206 scopus 로고    scopus 로고
    • On the geometric approach to the motion of inertial mechanical systems
    • Constantin A., Kolev B.: On the geometric approach to the motion of inertial mechanical systems. J. Phys. A 35(32), R51-R79 (2002).
    • (2002) J. Phys. A , vol.35 , Issue.32
    • Constantin, A.1    Kolev, B.2
  • 8
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • Constantin A., Kolev B.: Geodesic flow on the diffeomorphism group of the circle. Comment. Math. Helv. 78(4), 787-804 (2003).
    • (2003) Comment. Math. Helv. , vol.78 , Issue.4 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 9
    • 60349102715 scopus 로고    scopus 로고
    • The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
    • Constantin A., Lannes D.: The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations. Arch. Ration. Mech. Anal. 192(1), 165-186 (2009).
    • (2009) Arch. Ration. Mech. Anal. , vol.192 , Issue.1 , pp. 165-186
    • Constantin, A.1    Lannes, D.2
  • 10
    • 0036441096 scopus 로고    scopus 로고
    • A new integrable equation with peakon solutions
    • Degasperis A., Holm D. D., Hone A. N. I.: A new integrable equation with peakon solutions. Teoret. Mat. Fiz. 133(2), 170-183 (2002).
    • (2002) Teoret. Mat. Fiz. , vol.133 , Issue.2 , pp. 170-183
    • Degasperis, A.1    Holm, D.D.2    Hone, A.N.I.3
  • 12
    • 84870408969 scopus 로고    scopus 로고
    • Existence de géodésiques d'un groupe de difféomorphismes muni d'une métrique de Sobolev
    • Djebali S., Hermas N.: Existence de géodésiques d'un groupe de difféomorphismes muni d'une métrique de Sobolev. Afr. Diaspora J. Math. 9, 50-63 (2010).
    • (2010) Afr. Diaspora J. Math. , vol.9 , pp. 50-63
    • Djebali, S.1    Hermas, N.2
  • 13
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of an incompressible fluid
    • Ebin D. G., Marsden J.: Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. Math. 92(2), 102-163 (1970).
    • (1970) Ann. Math. , vol.92 , Issue.2 , pp. 102-163
    • Ebin, D.G.1    Marsden, J.2
  • 14
    • 34548219119 scopus 로고    scopus 로고
    • Wave breaking and shock waves for a periodic shallow water equation
    • Escher J.: Wave breaking and shock waves for a periodic shallow water equation. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 365(1858), 2281-2289 (2007).
    • (2007) Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. , vol.365 , Issue.1858 , pp. 2281-2289
    • Escher, J.1
  • 16
    • 34247509833 scopus 로고    scopus 로고
    • Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation
    • Escher J., Liu Y., Yin Z.: Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation. Indiana Univ. Math. J. 56(1), 87-117 (2007).
    • (2007) Indiana Univ. Math. J. , vol.56 , Issue.1 , pp. 87-117
    • Escher, J.1    Liu, Y.2    Yin, Z.3
  • 17
    • 77955234722 scopus 로고    scopus 로고
    • The periodic b-equation and Euler equations on the circle
    • Escher, J., Seiler, J.: The periodic b-equation and Euler equations on the circle. J. Math. Phys. 51: 053101. 1-053101. 6 (2010).
    • (2010) J. Math. Phys , vol.51
    • Escher, J.1    Seiler, J.2
  • 18
    • 55249108067 scopus 로고    scopus 로고
    • Well-posedness, blow-up phenomena, and global solutions for the b-equation
    • Escher J., Yin Z.: Well-posedness, blow-up phenomena, and global solutions for the b-equation. J. Reine Angew. Math. 624, 51-80 (2008).
    • (2008) J. Reine Angew. Math. , vol.624 , pp. 51-80
    • Escher, J.1    Yin, Z.2
  • 20
    • 84966236065 scopus 로고
    • The inverse function theorem of Nash and Moser
    • Hamilton R. S.: The inverse function theorem of Nash and Moser. Bull. Amer. Math. Soc. (N. S.) 7(1), 65-222 (1982).
    • (1982) Bull. Amer. Math. Soc. (N.S.) , vol.7 , Issue.1 , pp. 65-222
    • Hamilton, R.S.1
  • 21
    • 0037275227 scopus 로고    scopus 로고
    • Prolongation algebras and Hamiltonian operators for peakon equations
    • Hone A. N. W., Wang J. P.: Prolongation algebras and Hamiltonian operators for peakon equations. Inverse Problems 19(1), 129-145 (2003).
    • (2003) Inverse Problems , vol.19 , Issue.1 , pp. 129-145
    • Hone, A.N.W.1    Wang, J.P.2
  • 22
    • 26444571289 scopus 로고    scopus 로고
    • On the integrability of a class of nonlinear dispersive waves equations
    • Ivanov R. I.: On the integrability of a class of nonlinear dispersive waves equations. J. Nonlinear Math. Phys. 12(4), 462-468 (2005).
    • (2005) J. Nonlinear Math. Phys. , vol.12 , Issue.4 , pp. 462-468
    • Ivanov, R.I.1
  • 24
    • 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, 63-82 (2002).
    • (2002) J. Fluid Mech. , vol.455 , pp. 63-82
    • Johnson, R.S.1
  • 25
    • 0038455796 scopus 로고    scopus 로고
    • The classical problem of water waves: a reservoir of integrable and nearly-integrable equations
    • Johnson R. S.: The classical problem of water waves: a reservoir of integrable and nearly-integrable equations. J. Nonlinear Math. Phys. 10(1), 72-92 (2003).
    • (2003) J. Nonlinear Math. Phys. , vol.10 , Issue.1 , pp. 72-92
    • Johnson, R.S.1
  • 26
    • 70249137567 scopus 로고    scopus 로고
    • Some geometric investigations on the Degasperis-Procesi shallow water equation
    • Kolev B.: Some geometric investigations on the Degasperis-Procesi shallow water equation. Wave Motion 46, 412-419 (2009).
    • (2009) Wave Motion , vol.46 , pp. 412-419
    • Kolev, B.1
  • 27
    • 0033483085 scopus 로고    scopus 로고
    • The Camassa-Holm equation as a geodesic flow on the diffeomorphism group
    • Kouranbaeva S.: The Camassa-Holm equation as a geodesic flow on the diffeomorphism group. J. Math. Phys. 40(2), 857-868 (1999).
    • (1999) J. Math. Phys. , vol.40 , Issue.2 , pp. 857-868
    • Kouranbaeva, S.1
  • 28
    • 0003263328 scopus 로고    scopus 로고
    • Fundamentals of differential geometry
    • Springer, New York
    • Lang, S.: Fundamentals of differential geometry. Graduate Texts in Mathematics, vol. 191. Springer, New York (1999).
    • (1999) Graduate Texts In Mathematics , vol.191
    • Lang, S.1
  • 30
    • 85045532817 scopus 로고    scopus 로고
    • Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach
    • Birkhäuser Boston, Boston, MA
    • Michor, P. W.: Some geometric evolution equations arising as geodesic equations on groups of diffeomorphisms including the Hamiltonian approach. Phase space analysis of partial differential equations, Progr. Nonlinear Differential Equations Appl., vol. 69, pp. 133-215. Birkhäuser Boston, Boston, MA (2006).
    • (2006) Phase Space Analysis of Partial Differential Equations, Progr. Nonlinear Differential Equations Appl , vol.69 , pp. 133-215
    • Michor, P.W.1
  • 31
    • 0037036176 scopus 로고    scopus 로고
    • Perturbative symmetry approach
    • Mikhailov A. V., Novikov V. S.: Perturbative symmetry approach. J. Phys. A 35(22), 4775-4790 (2002).
    • (2002) J. Phys. A , vol.35 , Issue.22 , pp. 4775-4790
    • Mikhailov, A.V.1    Novikov, V.S.2
  • 33
    • 34548239768 scopus 로고
    • Une méthode de "cinématique fonctionnelle" en hydrodynamique
    • Moreau J. J.: Une méthode de "cinématique fonctionnelle" en hydrodynamique. C. R. Acad. Sci. Paris 249, 2156-2158 (1959).
    • (1959) C. R. Acad. Sci. Paris , vol.249 , pp. 2156-2158
    • Moreau, J.J.1
  • 34


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.