We compute arbitrary-order asymptotic expansions of standing water waves, generalizing the conformal mapping framework of Schwartz and Whitney (1981) to handle finite-depth domains and/or surface tension effects. The calculations are performed in arbitrary precision and parallelized to run on a supercomputer. We explore Pade approximations of the expansions and observe branch cuts that leave gaps in the families of solutions. We also explore analytic continuation of standing waves into the upper half-plane and observe branch cuts there as well.

This is joint work with Ahmad Abassi (UC Berkeley).