3 papers
math.AP2026
Local well-posedness of spatially quasiperiodic gravity water waves in two dimensions
Mihaela Ifrim, Jon Wilkening, Xinyu Zhao
We provide the first proof of local well-posedness for the two-dimensional gravity water wave equations with spatially quasi-periodic initial conditions. We represent the solution…
physics.flu-dyn2025
The semi-analytic theory and computation of finite-depth standing water waves
Ahmad Abassi, Jon Wilkening
We propose a Stokes expansion ansatz for finite-depth standing water waves in two dimensions and devise a recursive algorithm to compute the expansion coefficients. We implement th…
math.NA2024
Analyticity and Stable Computation of Dirichlet-Neumann Operators for Laplace's Equation under Quasiperiodic Boundary Conditions in Two and Three Dimensions
David P. Nicholls, Jon Wilkening, Xinyu Zhao
Dirichlet-Neumann Operators (DNOs) are important to the formulation, analysis, and simulation of many crucial models found in engineering and the sciences. For instance, these oper…