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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 838302, 6 pages
The Global Weak Solution for a Generalized Camassa-Holm Equation
Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan 610074, China
Received 25 October 2012; Accepted 24 December 2012
Academic Editor: Yong Hong Wu
Copyright © 2013 Shaoyong Lai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. Camassa and D. D. Holm, “An integrable shallow water equation with peaked solitons,” Physical Review Letters, vol. 71, no. 11, pp. 1661–1664, 1993.
- R. S. Johnson, “Camassa-Holm, Korteweg-de Vries and related models for water waves,” Journal of Fluid Mechanics, vol. 455, no. 1, pp. 63–82, 2002.
- R. S. Johnson, “On solutions of the Camassa-Holm equation,” Proceedings of the Royal Society A, vol. 459, no. 2035, pp. 1687–1708, 2003.
- A. Fokas and B. Fuchssteiner, “Symplectic structures, their Bäcklund transformations and hereditary symmetries,” Physica D, vol. 4, no. 1, pp. 47–66, 1981.
- A. Constantin and D. Lannes, “The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations,” Archive for Rational Mechanics and Analysis, vol. 192, no. 1, pp. 165–186, 2009.
- A. Constantin, “On the scattering problem for the Camassa-Holm equation,” Proceedings of the Royal Society A, vol. 457, no. 2008, pp. 953–970, 2001.
- J. Lenells, “Conservation laws of the Camassa-Holm equation,” Journal of Physics A, vol. 38, no. 4, pp. 869–880, 2005.
- H. P. McKean, “Fredholm determinants and the Camassa-Holm hierarchy,” Communications on Pure and Applied Mathematics, vol. 56, no. 5, pp. 638–680, 2003.
- A. Constantin and J. Escher, “Global existence and blow-up for a shallow water equation,” Annali della Scuola Normale Superiore di Pisa, vol. 26, no. 2, pp. 303–328, 1998.
- A. Constantin, “Existence of permanent and breaking waves for a shallow water equation: a geometric approach,” Annales de l'Institut Fourier, vol. 50, no. 2, pp. 321–362, 2000.
- A. Constantin, “On the inverse spectral problem for the Camassa-Holm equation,” Journal of Functional Analysis, vol. 155, no. 2, pp. 352–363, 1998.
- A. Constantin and J. Escher, “Global weak solutions for a shallow water equation,” Indiana University Mathematics Journal, vol. 47, no. 4, pp. 1527–1545, 1998.
- A. Constantin and B. Kolev, “Geodesic flow on the diffeomorphism group of the circle,” Commentarii Mathematici Helvetici, vol. 78, no. 4, pp. 787–804, 2003.
- A. Constantin, T. Kappeler, B. Kolev, and P. Topalov, “On geodesic exponential maps of the Virasoro group,” Annals of Global Analysis and Geometry, vol. 31, no. 2, pp. 155–180, 2007.
- S. Y. Lai and Y. H. Wu, “The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation,” Journal of Differential Equations, vol. 248, no. 8, pp. 2038–2063, 2010.
- S. Y. Lai and Y. H. Wu, “A model containing both the Camassa-Holm and Degasperis-Procesi equations,” Journal of Mathematical Analysis and Applications, vol. 374, no. 2, pp. 458–469, 2011.
- S. Y. Lai and Y. H. Wu, “Existence of weak solutions in lower order Sobolev space for a Camassa-Holm-type equation,” Journal of Physics A, vol. 43, no. 9, Article ID 095205, 13 pages, 2010.
- A. Bressan and A. Constantin, “Global conservative solutions of the Camassa-Holm equation,” Archive for Rational Mechanics and Analysis, vol. 183, no. 2, pp. 215–239, 2007.
- A. Bressan and A. Constantin, “Global dissipative solutions of the Camassa-Holm equation,” Analysis and Applications, vol. 5, no. 1, pp. 1–27, 2007.
- N. Li, S. Y. Lai, S. Li, and M. Wu, “The local and global existence of solutions for a generalized Camassa-Holm equation,” Abstract and Applied Analysis, vol. 2012, Article ID 532369, 26 pages, 2012.
- B. Kolev, “Poisson brackets in hydrodynamics,” Discrete and Continuous Dynamical Systems A, vol. 19, no. 3, pp. 555–574, 2007.