| Abstract: |
| Periodic travelling waves that solve the capillary-gravity Whitham equation have been fully characterised in the case of small and even waves. This characterisation is complemented by the work presented in this talk dealing with small asymmetric periodic travelling waves. Such asymmetric waves are far more scarce than the even ones and can only be constructed in certain cases for weak surface tension. The method also generalises in a straightforward way to a class of similar equations for which we either can prove the existence of or non-existence of asymmetric solutions. However, the proof relies on some technical calculations that are different for each equation. We note how this could be done for the Babenko equation, which is equivalent to the full water wave problem, to determine the existence of small amplitude Capillary-Gravity Waves. |
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