# Long Wave Approximations for Water Waves

```@article{Bona2005LongWA,
title={Long Wave Approximations for Water Waves},
author={Jerry L. Bona and Thierry Colin and David Lannes},
journal={Archive for Rational Mechanics and Analysis},
year={2005},
volume={178},
pages={373-410}
}```
• Published 21 June 2005
• Mathematics
• 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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