| Abstract: |
| 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 with up to 3000 bits using MPFR 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. |
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