Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water

The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary waves on infinite depth is extended to the general case of non-symmetric solutions. We have calculated non-symmetric steady periodic gravity-capillary waves on deep water. It is found that they appear via bifurcations from a family of symmetric waves. On the other hand we found that the symmetry-breaking bifurcation of periodic steady class 1 gravity wave on deep water is possible when it approaches the limiting profile, if it is very weakly influenced by surface tension effects. To cite this article: R. Aider, M. Debiane, C. R. Mecanique 332 (2004).