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Waves in shallow water, with emphasis on the tsunami of 2004

  • Harvey Segur

Abstract

This conference was organized in response to the 2004 tsunami, which killed nearly 300,000 people in coastal communities around the Indian Ocean. We can expect more tsunamis in the future, so now is a good time to think carefully about how to prepare for the next tsunami. With that objective, this paper addresses three broad questions about tsunamis.

Keywords

Indian Ocean Shallow Water Water Wave Wave Volume Steep Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Ablowitz MJ, Segur H (1981) Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, PAGoogle Scholar
  2. [2]
    Boussinesq J (1871) Theorie de l’intumescence liquide appele onde solitaire.... Comptes Rendus 72:755–759Google Scholar
  3. [3]
    Camassa R, Holm DD (1993) An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71:1661–1664CrossRefGoogle Scholar
  4. [4]
    Carrier, GF, Greenspan HP (1958) Water waves of finite amplitude on a sloping beach. J. Fluid Mech. 4:97–109CrossRefGoogle Scholar
  5. [5]
    Carrier GF, Wu TT, Yeh, H (2003) Tsunami runup and drawdown on a plane beach. J. Fluid Mech. 475:79–99CrossRefGoogle Scholar
  6. [6]
    Hammack JL (1973) A note on tsunamis: their generation and propagation in an ocean of uniform depth. J. Fluid Mech. 60:769–800CrossRefGoogle Scholar
  7. [7]
    Hammack JL, Segur H (1974) The Korteweg-deVries equation and water waves, part 2. Comparison with experiments. J. Fluid Mech. 65:289–314CrossRefGoogle Scholar
  8. [8]
    Hammack JL, Segur H (1978a) The Korteweg-deVries equation and water waves, part 3. Oscillatory waves. J. Fluid Mech. 84:337–358CrossRefGoogle Scholar
  9. [9]
    Hammack JL, Segur H (1978b) Modelling criteria for long water waves. J. Fluid Mech., 84:359–373CrossRefGoogle Scholar
  10. [10]
    Johnson RS (1997) An Introduction to the Mathematical Theory of Water Waves, Cambridge Univ. PressGoogle Scholar
  11. [11]
    Kadomtsev BB, Petviashvili VI (1970) On the stability of solitary waves in weakly dispersive media. Sov. Phys. Doklady 15:539–541Google Scholar
  12. [12]
    Korteweg DJ, de Vries G (1895) On the change of form of long waves advancing in a rectangular canal. Philos. Mag. Ser. 5,39:422–443Google Scholar
  13. [13]
    Lakshmanan M, Rajasekar R (2003) Nonlinear Dynamics — Integrability, Chaos and Patterns, Springer, NYGoogle Scholar
  14. [14]
    Scott AC (1999) Nonlinear Science: Emergence and Dynamics of Coherent Structures, Oxford Univ. Press, NYGoogle Scholar
  15. [15]
    Stoker JJ (1957) Water Waves. Wiley Interscience, NYGoogle Scholar
  16. [16]
    Stokes GG (1847) On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8:441–455Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Harvey Segur
    • 1
  1. 1.Department of Applied MathematicsUniversity of ColoradoBoulderUSA

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