Stability of the Camassa-Holm solitons

Journal of Nonlinear Science

Volumn 12, Issue 4, 2002, Pages 415-422

  Constantin, A ^a   Strauss, W A ^b  

^a LUND UNIVERSITY   (Sweden)

^b BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000380413     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00332-002-0517-x     Document Type: Article

References (19)

1. R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71(1993), 1661-1664.
2. R. Camassa, D. Holm, and J. Hyman, A new integrable shallow water equation, Adv. Appl. Mech. 31(1994), 1-33.
3. A. Constantin, On the scattering problem for the Camassa-Holm equation, Proc. Roy. Soc. London 457(2001), 953-970.
4. A. Constantin and J. Escher, Global existence and blow-up for a shallow water equation, Annali Sc. Norm. Sup. Pisa 26(1998), 303-328.
5. A. Constantin and W. Strauss, Stability of peakons, Commun. Pure Appl. Math. 53(2000), 603-610.
6. P. Drazin and R. S. Johnson, Solitons: An Introduction (Cambridge Univ. Press, Cambridge, 1989).
7. N. Dunford and J. T. Schwartz, Linear Operators, vol. 2 (Wiley, New York, 1988).
8. A. S. Fokas, On a class of physically important integrable equations, Physica D 87(1995), 145-150.
9. B. Fuchssteiner and A. S. Fokas, Symplectic structures, their Bäcklund transformation and hereditary symmetries, Physica D 4(1981), 47-66.
10. B. Fuchssteiner, Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation, Physica D 95(1996), 229-243.
11. M. Grillakis, J. Shatah, and W. Strauss, Stability theory of solitary waves in the presence of symmetry, J. Funct. Anal. 74(1987), 160-197.
12. D. Holm, J. Marsden, and T. Ratiu, The Euler-Poincaré equations and semidirect products with applications to continuum theories, Adv. Math. 137(1998), 1-81.
13. R. S. Johnson, Camassa-Holm, Korteweg-de Vries, and related models for water waves, J. Fluid Mech. 455(2002), 63-82.
14. P. Lax, Outline of a theory of the KdV equation, Springer Lecture Notes in Math. 1640(1996), 70-112.
15. Y. Li and P. Olver, Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system, Discrete Cont. Dyn. Syst. 3(1997), 419-432.
16. Y. Li and P. Olver, Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation, J. Diff. Eq. 162(2000), 27-63.
17. H. P. McKean, Breakdown of a shallow water equation, Asian J. Math. 2(1998), 867-879.
18. G. Misiolek, A shallow water equation as a geodesic flow on the Bott-Virasoro group, J. Geom. Phys. 24(1998), 203-208.
19. V. Zakharov and L. Faddeev, Korteweg-de Vries equation: A completely integrable Hamiltonian system, Funct. Anal. Appl. 5(1971), 280-287.