Euler-poincaré models of ideal fluids with nonlinear dispersion

Physical Review Letters

Volumn 80, Issue 19, 1998, Pages 4173-4176

  Holm, Darryl D ^a   Marsden, Jerrold E ^b   Ratiu, Tudor S ^c  

^a CENTER FOR NONLINEAR STUDIES   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11744318899     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.80.4173     Document Type: Article

References (24)

1. I. Gjaja and D. D. Holm, Physica (Amsterdam), 98D, 343–378 (1996).
2. R. Camassa and D. D. Holm, Phys. Rev. Lett., 71, 1661–1664 (1993).
3. R. Camassa, D. D. Holm, and J. M. Hyman, Advances in Applied Mechanics (Academic Press, Boston, 1994), Vol., 31, pp. 1–33.
4. M. Alber, R. Camassa, D. D. Holm, and J. E. Marsden, Lett. Math. Phys., 32, 137–151 (1994).
5. M. Alber, R. Camassa, D. D. Holm, and J. E. Marsden, Proc. R. Soc., 450, 677–692 (1995).
6. F. Calogero, Phys. Lett. A, 201, 306–310 (1995).
7. F. Calogero and J. P. Francoise, J. Math. Phys. (N.Y.), 37, 2863–2871 (1996).
8. O. Ragnisco and M. Bruschi, Physica (Amsterdam), 228A, 150–159 (1996).
9. Y. B. Suris, Phys. Lett. A, 217, 321–329 (1996).
10. B. Fuchssteiner, Physica (Amsterdam), 95D, 229–243 (1996).
11. J. Schiff, “The Camassa-Holm Equation: A Loop Group Approach” (to be published).
12. G. Misiolek, “A Shallow Water Equation as a Geodesic Flow on the Bott-Virasoro Group” (to be published).
13. J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry, Texts in Applied Mathematics Vol., 17 (Springer, New York, 1994).
14. D. D. Holm, J. E. Marsden, and T. S. Ratiu, “Euler-Poincaré Equations and Semidirect Products with Applications to Continuum Theories,” Adv. Math. (to be published).
15. J. Pedlosky, Geophysical Fluid Dynamics (Springer, New York, 1987), 2nd ed.
16. V. I. Arnold, Ann. Inst. Fourier, Grenoble, 16, 319–361 (1966).
17. D. G. Andrews and M. E. McIntyre, J. Fluid Mech., 89, 609-646 (1978).
18. H. D. I. Abarbanel, D. D. Holm, J. E. Marsden, and T. Ratiu, Philos. Trans. R. Soc. London A, 318, 349–409 (1986).
19. J. E. Dunn and R. L. Fosdick, Arch. Ration. Mech. Anal., 56, 191–252 (1974).
20. D. Cioranescu and V. Girault, C. R. Acad. Sci. Paris Série 1, 322, 1163–1168 (1996).
21. D. Cioranescu and V. Girault, Int. J. Non-Linear Mech., 32, 317–335 (1997).
22. S. Y. Chen, C. Foias, D. D. Holm, E. Olson, E. S. Titi, and S. Wynne, “The Steady Viscous Camassa-Holm Equations as a Reynolds Algebraic Stress Closure Model for Turbulent Channel Flows and Their Boundary Layer Analysis” (to be published).
23. D. D. Holm, R. Kinney, and J. C. McWilliams, “Vortex Interaction in Planar α Models” (to be published).
24. D. D. Holm, S. Kouranbaeva, J. E. Marsden, T. Ratiu, and S. Shkoller, “Euler-Poincaré Equations for Continuum Theories on Riemannian Manifolds” (to be published).