On finite amplitude water waves

  • G. B. Whitham


The modulation theory for finite amplitude water waves is developed using the variational technique. It is shown how Levi-Civita’s relation, Starr’s relation and the conservation equations all follow very simply and naturally from this approach. The present paper is limited to deep water waves, but the results can be extended to arbitrary depth. For deep water, the appropriate Lagrangian can be reduced to a single function, which can be taken from recent numerical calculations on periodic waves. This is used to discuss the stability of wavetrains to long modulations.


Water waves nonlinear waves variational methods 


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  1. Longuet-Higgins M S 1975Proc. R. Soc. London)A342 57MathSciNetGoogle Scholar
  2. Starr V P 1947J. Mar. Res. 6 75Google Scholar
  3. Whitham G B 1974Linear and nonlinear waves (New York: Wiley-Interscience)MATHGoogle Scholar

Copyright information

© Indian Academy of Sciences 1982

Authors and Affiliations

  • G. B. Whitham
    • 1
  1. 1.Department of Applied MathematicsCalifornia Institute of TechnologyPasadenaUSA

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