Long Wave Approximations for Water Waves

  title={Long Wave Approximations for Water Waves},
  author={Jerry L. Bona and Thierry Colin and David Lannes},
  journal={Archive for Rational Mechanics and Analysis},
In this paper, we obtain new nonlinear systems describing the interaction of long water waves in both two and three dimensions. These systems are symmetric and conservative. Rigorous convergence results are provided showing that solutions of the complete free-surface Euler equations tend to associated solutions of these systems as the amplitude becomes small and the wavelength large. Using this result as a tool, a rigorous justification of all the two-dimensional, approximate systems recently… 

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  • T. BenjaminJ. BonaJ. Mahony
  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1972
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  • J. BonaRonald Smith
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1976
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