336 citations · 1.2k across the 44 of their papers we have counts for
48 papers
Self-similarity and recurrence in stability spectra of near-extreme Stokes waves
Bernard Deconinck, Sergey A. Dyachenko, Anastassiya Semenova
We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree c…
The instability of near-extreme Stokes waves
Bernard Deconinck, Sergey A. Dyachenko, Pavel M. Lushnikov +1
We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growt…
Solving the heat equation with variable thermal conductivity
Matthew Farkas, Bernard Deconinck
We consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we…
The analytic extension of solutions to initial-boundary value problems outside their domain of definition
Matthew Farkas, Jorge Cisneros, Bernard Deconinck
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transf…
A High-Order Asymptotic Analysis of the Benjamin-Feir Instability Spectrum in Arbitrary Depth
Ryan Creedon, Bernard Deconinck
We investigate the Benjamin-Feir (or modulational) instability of Stokes waves, i.e., small-amplitude, one-dimensional periodic gravity waves of permanent form and constant velocit…
The numerical solution of semidiscrete linear evolution problems on the finite interval using the Unified Transform Method
Jorge Cisneros, Bernard Deconinck
We study a semidiscrete analogue of the Unified Transform Method introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential equat…