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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 480670, 7 pages
http://dx.doi.org/10.1155/2014/480670
Research Article

On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current

1School of Science, Southwest Petroleum University, Chengdu, Sichuan 610500, China
2State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China

Received 20 January 2014; Revised 25 March 2014; Accepted 27 March 2014; Published 14 April 2014

Academic Editor: Ricardo Weder

Copyright © 2014 Dali Guo et al. 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.

Linked References

  1. J. A. Simmen, Steady deep-water waves on a linear shear current [Ph.D. thesis], 1984.
  2. A. F. Teles da Silva and D. H. Peregrine, “Steep, steady surface waves on water of finite depth with constant vorticity,” Journal of Fluid Mechanics, vol. 195, pp. 281–302, 1988.
  3. J.-M. Vanden-Broeck, “Steep solitary waves in water of finite depth with constant vorticity,” Journal of Fluid Mechanics, vol. 274, pp. 339–348, 1994. View at Scopus
  4. J.-M. Vanden-Broeck, “Periodic waves with constant vorticity in water of infinite depth,” IMA Journal of Applied Mathematics, vol. 56, no. 3, pp. 207–217, 1996. View at Scopus
  5. A. Constantin, D. Sattinger, and W. Strauss, “Variational formulations for steady water waves with vorticity,” Journal of Fluid Mechanics, vol. 548, pp. 151–163, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. A. Constantin and W. Strauss, “Exact steady periodic water waves with vorticity,” Communications on Pure and Applied Mathematics, vol. 57, no. 4, pp. 481–527, 2004. View at Scopus
  7. J. Ko and W. Strauss, “Effect of vorticity on steady water waves,” Journal of Fluid Mechanics, vol. 608, pp. 197–215, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. E. Wahlén, “Steady periodic capillary-gravity waves with vorticity,” SIAM Journal on Mathematical Analysis, vol. 38, no. 3, pp. 921–943, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Biello and J. K. Hunter, “Nonlinear Hamiltonian waves with constant frequency and surface waves on vorticity discontinuities,” Communications on Pure and Applied Mathematics, vol. 63, no. 3, pp. 303–336, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Constantin, R. I. Ivanov, and E. M. Prodanov, “Nearly-Hamiltonian structure for water waves with constant vorticity,” Journal of Mathematical Fluid Mechanics, vol. 10, no. 2, pp. 224–237, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. E. Wahlén, “A Hamiltonian formulation of water waves with constant vorticity,” Letters in Mathematical Physics, vol. 79, no. 3, pp. 303–315, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. A. I. Dyachenko, V. E. Zakharov, and E. A. Kuznetsov, “Nonlinear dynamics of the free surface of an ideal fluid,” Plasma Physics Reports, vol. 22, no. 10, pp. 829–840, 1996. View at Scopus
  13. W. Choi, “Nonlinear surface waves interacting with a linear shear current,” Mathematics and Computers in Simulation, vol. 80, no. 1, pp. 29–36, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. P. A. Milewski, J.-M. Vanden-Broeck, and Z. Wang, “Dynamics of steep two-dimensional gravity-capillary solitary waves,” Journal of Fluid Mechanics, vol. 664, pp. 466–477, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. Y. Kang and J.-M. Vanden-Broeck, “Gravity-capillary waves in the presence of constant vorticity,” European Journal of Mechanics, B, vol. 19, no. 2, pp. 253–268, 2000. View at Publisher · View at Google Scholar · View at Scopus
  16. J.-M. Vanden-Broeck and F. Dias, “Gravity-capillary solitary waves in water of infinite depth and related free-surface flows,” Journal of Fluid Mechanics, vol. 240, pp. 549–557, 1992. View at Scopus