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

Ben Segal (2017)

Natalie Sheils (2015, Postdoc at U. of Minnesota)

Olga Trichtchenko (2014, Postdoc at UCL, London)

(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

1. Solving the heat equation with variable thermal conductivity (with M. Farkas), (submitted for publication, 2022) .pdf
2. 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
3. A High-Order Asymptotic Analysis of the Benjamin-Feir Instability Spectrum in Arbitrary Depth (with R. Creedon), (submitted for publication, 2022) .pdf
4. 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
5. High-Frequency Instabilities of Stokes Waves (with R. Creedon and O. Trichtchenko), (submitted for publication, 2021) .pdf (Note: the full submission, including Mathematica files, can be found on the arxiv) .pdf"> .pdf.

(Additional Publications)

Software Development

1. Riemann Constant Vector. Maple software for the computation of the Riemann Constant Vector of a Riemann surface specified as a plane algebraic curve.
2. SpectrUW 2.0:Freeware for the computation of spectra of linear operators.

(All Software)