25 citations · 62 across the 6 of their papers we have counts for
6 papers
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…
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…
Spatially quasi-periodic water waves of finite depth
Jon Wilkening, Xinyu Zhao
We present a numerical study of spatially quasi-periodic gravity-capillary waves of finite depth in both the initial value problem and traveling wave settings. We adopt a quasi-per…
Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values
Jon Wilkening, Xinyu Zhao
We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent…
Quasi-periodic traveling gravity-capillary waves
Jon Wilkening, Xinyu Zhao
We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple p…
Spatially quasi-periodic water waves of infinite depth
Jon Wilkening, Xinyu Zhao
We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value proble…