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Mat. Zametki, 2007, Volume 81, Issue 1, Pages 149–152 (Mi mz3528)  

This article is cited in 17 scientific papers (total in 17 papers)

Brief Communications

Two-Component Generalizations of the Camassa–Holm Equation

P. A. Kuzmin

M. V. Lomonosov Moscow State University

Keywords: Camassa–Holm equation, bi-Hamiltonian system, group of diffeomorphisms of the circle, coadjoint orbit, Virasoro cocycle, Lie–Poisson structure

DOI: https://doi.org/10.4213/mzm3528

Full text: PDF file (265 kB)
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English version:
Mathematical Notes, 2007, 81:1, 130–134

Bibliographic databases:

Received: 12.04.2006

Citation: P. A. Kuzmin, “Two-Component Generalizations of the Camassa–Holm Equation”, Mat. Zametki, 81:1 (2007), 149–152; Math. Notes, 81:1 (2007), 130–134

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gibbons J., Holm D. D., Tronci C., “Vlasov moments, integrable systems and singular solutions”, Phys. Lett. A, 372:7 (2008), 1024–1033  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Holm D. D., Ó Náraigh L., Tronci C., “Singular solutions of a modified two-component Camassa-Holm equation”, Phys. Rev. E, 79:1 (2009), 016601, 13 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    3. Fan E., “The positive and negative Camassa-Holm-$\gamma$ hierarchies, zero curvature representations, bi-Hamiltonian structures, and algebro-geometric solutions”, J. Math. Phys., 50:1 (2009), 013525, 23 pp.  crossref  mathscinet  adsnasa  isi  scopus
    4. Holm D.D., Tronci C., “Geodesic flows on semidirect-product Lie groups: geometry of singular measure-valued solutions”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 465:2102 (2009), 457–476  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Holm D.D., Trouvé A., Younes L., “The Euler-Poincaré theory of metamorphosis”, Quart. Appl. Math., 67:4 (2009), 661–685  crossref  mathscinet  zmath  isi  elib  scopus
    6. Holm D.D., Tronci C., “Geodesic Vlasov equations and their integrable moment closures”, J. Geom. Mech., 1:2 (2009), 181–208  crossref  mathscinet  zmath  isi
    7. Holm D.D., Ivanov R.I., “Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples”, J. Phys. A, 43:49 (2010), 492001, 20 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    8. Holm D.D., Ivanov R.I., “Two-component CH system: inverse scattering, peakons and geometry”, Inverse Problems, 27:4 (2011), 045013  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Grunert K., Holden H., Raynaud X., “Global solutions for the two-component Camassa-Holm system”, Commun. Partial Differ. Equ., 37:12 (2012), 2245–2271  crossref  zmath  isi  elib  scopus
    10. Xie Sh., Zhang Yu., He J., “Two Types of Bounded Traveling-Wave Solutions of a Two-Component Camassa-Holm Equation”, Appl. Math. Comput., 219:20 (2013), 10271–10282  crossref  mathscinet  zmath  isi  scopus
    11. Gay-Balmaz F., Tronci C., Vizman C., “Geometric Dynamics on the Automorphism Group of Principal Bundles: Geodesic Flows, Dual Pairs and Chromomorphism Groups”, J. Geom. Mech., 5:1 (2013), 39–84  crossref  mathscinet  zmath  isi  elib  scopus
    12. Gay-Balmaz F., Holm D.D., Ratiu T.S., “Geometric Dynamics of Optimization”, Commun. Math. Sci., 11:1 (2013), 163–231  crossref  mathscinet  zmath  isi  elib  scopus
    13. Guo Yu., Wang Y., “Wave-Breaking Criterion and Global Solution For a Generalized Periodic Coupled Camassa-Holm System”, Bound. Value Probl., 2014, 155  crossref  mathscinet  isi  scopus
    14. Grunert K., “Blow-Up For the Two-Component Camassa Holm System”, Discret. Contin. Dyn. Syst., 35:5 (2015), 2041–2051  crossref  mathscinet  zmath  isi  scopus
    15. Grunert K., Holden H., Raynaud X., “a Continuous Interpolation Between Conservative and Dissipative Solutions For the Two-Component Camassa-Holm System”, Forum Math. Sigma, 3 (2015), UNSP e1  crossref  mathscinet  isi
    16. Wang Y., “A wave breaking criterion for a modified periodic two-component Camassa-Holm system”, J. Inequal. Appl., 2016, 85  crossref  mathscinet  isi  scopus
    17. Pu Yu., Pego R.L., Dutykh D., Clamond D., “Weakly Singular Shock Profiles For a Non-Dispersive Regularization of Shallow-Water Equations”, Commun. Math. Sci., 16:5 (2018), 1361–1378  crossref  isi
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