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Table of contents for this issue  Next article Constantin, Adrian Existence of permanent and breaking waves for a shallow water equation : a geometric approach. Annales de l'institut Fourier, 50 no. 2 (2000), p. 321362 Full text djvu  pdf  Reviews MR 2002d:37125  Zbl 0944.35062  1 citation in Numdam stable URL: http://www.numdam.org/item?id=AIF_2000__50_2_321_0 Lookup this article on the publisher's site Abstract Bibliography Numdam  MR 34 #1956  Zbl 0148.45301 [2] V. ARNOLD and B. KHESIN, Topological Methods in Hydrodynamics, Springer Verlag, New York, [3] B. BENJAMIN and J. L. BONA and J. J. MAHONY, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Roy. Soc. London, 272 ( [4] R. CAMASSA and D. HOLM, An integrable shallow water equation with peaked solitons, Phys. Rev. Letters, 71 ( [5] R. CAMASSA and D. HOLM and J. HYMAN, A new integrable shallow water equation, Adv. Appl. Mech., 31 ( [6] M. CANTOR, Perfect fluid flows over Rn with asymptotic conditions, J. Funct. Anal., 18 ( [7] A. CONSTANTIN, The Cauchy problem for the periodic CamassaHolm equation, J. Differential Equations, 141 ( [8] A. CONSTANTIN and J. ESCHER, Wellposedness, global existence, and blowup phenomena for a periodic quasilinear hyperbolic equation, Comm. Pure Appl. Math., 51 ( [9] A. CONSTANTIN and J. ESCHER, Global existence and blowup for a shallow water equation, Annali Sc. Norm. Sup. Pisa, 26 ( Numdam  MR 99m:35202  Zbl 0918.35005 [10] A. CONSTANTIN and J. ESCHER, Wave breaking for nonlinear nonlocal shallow water equations, Acta Mathematica, 181 ( [11] A. CONSTANTIN and J. ESCHER, On the blowup rate and the blowup set of breaking waves for a shallow water equation, Math. Z., 233 ( [12] A. CONSTANTIN and H. P. MCKAN, A shallow water equation on the circle, Comm. Pure Appl. Math., 52 ( [13] J. DIEUDONNÉ, Foundations of Modern Analysis, Academic Press, New York, [14] R. K. DODD and J. C. EILBECK and J. D. GIBBON and H. C. MORRIS, Solitons and Nonlinear Wave Equations, Academic Press, New York, [15] P. G. DRAZIN and R. S. JOHNSON, Solitons: an Introduction, Cambridge University Press, Cambridge  New York, [16] D. EBIN and J. E. MARSDEN, Groups of diffeomorphisms and the notion of an incompressible fluid, Ann. of Math., 92 ( [17] L. EVANS and R. GARIEPY, Measure Theory and Fine Properties of Functions, Studies in Adv. Math., Boca Raton, Florida, [18] A. S. FOKAS and B. FUCHSSTEINER, Symplectic structures, their Bäcklund transformation and hereditary symmetries, Physica D, 4 ( [19] B. FUCHSSTEINER, Some tricks from the symmetrytoolbox for nonlinear equations: generalizations of the CamassaHolm equation, Physica D, 95 ( [20] T. KATO, Quasilinear equations of evolution, with applications to partial differential equations, Spectral Theory and Differential Equations, Springer Lecture Notes in Mathematics, 448 ( [21] C. KENIG and G. PONCE and L. VEGA, Wellposedness and scattering results for the generalized Kortewegde Vries equation via the contraction principle, Comm. Pure Appl. Math., 46 ( [22] D. J. KORTEWEG and G. de VRIES, On the change of form of long waves advancing in a rectangular channel, and on a new type of long stationary waves, Phil. Mag., 39 ( [23] S. KOURANBAEVA, The CamassaHolm equation as a geodesic flow on the diffeomorphism group, J. Math. Phys., 40 ( [24] S. LANG, Differential and Riemannian Manifolds, Springer Verlag, New York, [25] H. P. MCKEAN, Integrable systems and algebraic curves, Global Analysis, Springer Lecture Notes in Mathematics, 755 ( [26] J. MILNOR, Morse Theory, Ann. Math. Studies 53, Princeton University Press, [27] G. MISIOLEK, A shallow water equation as a geodesic flow on the BottVirasoro group, J. Geom. Phys., 24 ( [28] P. OLVER, Applications of Lie Groups to Differential Equations, Springer Verlag, NewYork, [29] E. M. STEIN and G. WEISS, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, [30] G. B. WHITHAM, Linear and Nonlinear Waves, J. Wiley & Sons, New York, 

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