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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 108026, 13 pages
http://dx.doi.org/10.1155/2013/108026
Research Article

Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth

1School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
2Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
3Research Center for Complex Systems and Network Sciences, Department of Mathematics, Southeast University, Nanjing 210096, China

Received 21 May 2013; Revised 29 August 2013; Accepted 29 August 2013

Academic Editor: Rasajit Bera

Copyright © 2013 Ping Wang and Zunshui Cheng. 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. A. G. Greenhill, “Wave motion in hydrodynamics,” American Journal of Mathematics, vol. 9, no. 1, pp. 62–96, 1886. View at Publisher · View at Google Scholar · View at MathSciNet
  2. V. A. Squire, J. P. Dugan, P. Wadhams, P. J. Rottier, and A. K. Liu, “Of ocean waves and sea ice,” Annual Review of Fluid Mechanics, vol. 27, pp. 115–168, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  3. V. A. Squire, “Of ocean waves and sea-ice revisited,” Cold Regions Science and Technology, vol. 49, no. 2, pp. 110–133, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. V. A. Squire, “Synergies between VLFS hydroelasticity and sea ice research,” International Journal of Offshore and Polar Engineering, vol. 18, no. 4, pp. 241–253, 2008. View at Scopus
  5. T. Kakinuma, K. Yamashita, and K. Nakayama, “Surface and internal waves due to a moving load on a very large floating structure,” Journal of Applied Mathematics, vol. 2012, Article ID 830530, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. F. Xu and D. Q. Lu, “Wave scattering by a thin elastic plate floating on a two-layer fluid,” International Journal of Engineering Science, vol. 48, no. 9, pp. 809–819, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. K. Forbes, “Surface waves of large amplitude beneath an elastic sheet. Part 1. High-order series solution,” Journal of Fluid Mechanics, vol. 169, pp. 409–428, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. K. Forbes, “Surface waves of large amplitude beneath an elastic sheet. Part 2. Galerkin solution,” Journal of Fluid Mechanics, vol. 188, pp. 491–508, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J.-M. Vanden-Broeck and E. I. Părău, “Two-dimensional generalized solitary waves and periodic waves under an ice sheet,” Philosophical Transactions of the Royal Society A, vol. 369, no. 1947, pp. 2957–2972, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S.-J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems [Ph. D. Dissertation], Shanghai Jiao Tong University, 1992.
  11. S.-J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Modern Mechanics and Mathematics, Chapman and Hall/ CRC Press, 1st edition, 2003.
  12. S.-J. Liao, Homotopy Analysis Method in Nonlinear Differential Equations, Springer & Higher Education Press, Heidelberg, Germany, 2003.
  13. S.-J. Liao, “On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet,” Journal of Fluid Mechanics, vol. 488, pp. 189–212, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S.-J. Liao and K. F. Cheung, “Homotopy analysis of nonlinear progressive waves in deep water,” Journal of Engineering Mathematics, vol. 45, no. 2, pp. 105–116, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Tao, H. Song, and S. Chakrabarti, “Nonlinear progressive waves in water of finite depth—an analytic approximation,” Coastal Engineering, vol. 54, no. 11, pp. 825–834, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. S.-J. Liao, “On the homotopy multiple-variable method and its applications in the interactions of nonlinear gravity waves,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1274–1303, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. D. Xu, Z. Lin, S.-J. Liao, and M. Stiassnie, “On the steady-state fully resonant progressive waves in water of finite depth,” Journal of Fluid Mechanics, vol. 710, pp. 379–418, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  18. J. Cheng and S. Q. Dai, “A uniformly valid series solution to the unsteady stagnation-point flow towards an impulsively stretching surface,” Science China, vol. 53, no. 3, pp. 521–526, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Abbasbandy, “The application of homotopy analysis method to nonlinear equations arising in heat transfer,” Physics Letters A, vol. 360, no. 1, pp. 109–113, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. S.-J. Liao and A. Campo, “Analytic solutions of the temperature distribution in Blasius viscous flow problems,” Journal of Fluid Mechanics, vol. 453, pp. 411–425, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. W. Wu and S.-J. Liao, “Solving solitary waves with discontinuity by means of the homotopy analysis method,” Chaos, Solitons and Fractals, vol. 26, no. 1, pp. 177–185, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. E. Sweet and R. A. van Gorder, “Analytical solutions to a generalized Drinfel'd-Sokolov equation related to DSSH and KdV,” Applied Mathematics and Computation, vol. 216, pp. 2783–2791, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  23. R. A. van Gorder, “Analytical method for the construction of solutions to the Föppl-von Kármán equations governing deflections of a thin flat plate,” International Journal of Non-Linear Mechanics, vol. 47, pp. 1–6, 2012.
  24. S.-J. Liao, “An optimal homotopy-analysis approach for strongly nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2003–2016, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. L. Zou, Z. Zong, Z. Wang, and L. He, “Solving the discrete KdV equation with homotopy analysis method,” Physics Letters A, vol. 370, no. 3-4, pp. 287–294, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. J. Cheng, S.-P. Zhu, and S.-J. Liao, “An explicit series approximation to the optimal exercise boundary of American put options,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 5, pp. 1148–1158, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. A. J. Roberts, “Highly nonlinear short-crested water waves,” Journal of Fluid Mechanics, vol. 135, pp. 301–321, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus