  In the present work we compute numerical solutions of an integro-differential
equation for traveling waves on the boundary of a $2$D blob of an ideal fluid
in the presence of surface tension. We find that solutions with multiple lobes
tend to approach Crapper capillary waves in the limit of many lobes. Solutions
with a few lobes become elongated as they become more nonlinear. It is unclear
whether there is a limiting solution for small number of lobes, and what are
its properties. Solutions are found from solving a nonlinear
pseudo--differential equation by means of the Newton-Conjugate Residual method.
We use Fourier basis to approximate the solution with the number of Fourier
modes up to $N = 65536$.
