The Semi-analytic Theory and Computation of Finite-depth Standing Water Waves

Ahmad Abassi, UC Berkeley

April 1, 2023 at 11:30am-12:30pm (Zoom: 972 8792 6728)

We generalize the semi-analytic standing-wave framework of Schwartz and Whitney (1981) and Amick and Toland (1987) to finite-depth standing gravity waves. We propose an appropriate Stokes-expansion ansatz and propose a recursive algorithm to solve the system of differential equations governing the expansion coefficients, which is then implemented on a supercomputer using arbitrary-precision arithmetic. Under mild assumptions, we prove no exact resonances occur using transcendental number theory, although small divisors do appear. We numerically investigate the effects of small divisors in relation to bifurcations and sudden changes in the growth rate of the expansion coefficients.