Bernard Deconinck's Research
- Research topics
- Analytical and numerical methods for nonlinear wave equations
- Current Projects
- Surface waves in water of arbitrary depth
- Finite-genus solutions of integrable equations
- Stability and instability of nonlinear waves
- Former Students
- Ryan Creedon (2022, instructor at U. of Washington)
- Jorge Cisneros (2022, postdoc at UT Austin)
- (more)
- Research Methods
-
The main topic of my research is the study of
nonlinear wave phenomena, especially with applications in water waves.
I use analytical techniques ranging from soliton theory and partial
differential equations to dynamical systems, perturbation theory and
Riemann surfaces. The computational methods I use cover a wide range
as well, from symbolic computation to continuation methods, data
analysis and spectral methods.
- Recent Publications
-
- The instability of near-extreme Stokes waves (with S. Dyachenko, P. Lushnikov \& A. Semenova),
(submitted for publication, 2022) .pdf
- Solving the heat equation with variable thermal conductivity (with M. Farkas),
(submitted for publication, 2022) .pdf
- The analytic extension of solutions to initial-boundary value
problems outside their domain of definition (with M. Farkas and J. Cisneros),
(submitted for publication, 2022) .pdf
- A High-Order Asymptotic Analysis of the Benjamin-Feir
Instability Spectrum in Arbitrary Depth (with R. Creedon),
(submitted for publication, 2022) .pdf
- The numerical solution of semidiscrete linear evolution problems on the finite interval
using the Unified Transform Method (with J. Cisneros),
(submitted for publication, 2021) .pdf
(Additional Publications)
- Software Development
-
- Riemann Constant Vector. Maple software for the computation of the Riemann Constant Vector of a Riemann surface specified as a plane algebraic curve.
- SpectrUW 2.0:Freeware for the computation of spectra of linear operators.
(All Software)