A note on solitary and cnoidal waves with surface tension

@article{VandenBroeck1983ANO,
  title={A note on solitary and cnoidal waves with surface tension},
  author={Jean-Marc Vanden-Broeck and M. C. Shen},
  journal={Zeitschrift f{\"u}r angewandte Mathematik und Physik ZAMP},
  year={1983},
  volume={34},
  pages={112-117}
}
SummaryThe influence of surface tension on solitary and cnoidal waves is considered. A first order perturbation solution is presented.RésuméL'effet de la tension superficielle sur les ondes solitaires et cnoidales est considéré. Un calcul de perturbation limité au premier ordre est présenté. 
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References

SHOWING 1-4 OF 4 REFERENCES
XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
(1895). XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of
Solitary waves in liquids having nonconstant density, Comm
  • Pure App. Math.,
  • 1960