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

1. The explicit solution of linear, dissipative, second-order initial-boundary value problems with variable coefficients (with M. farkas), (submitted for publication, 2024) .pdf
2. Selfsimilarity and recurrence in stability spectra of near-extreme Stokes waves (with S. Dyachenko and A. Semenova), (submitted for publication, 2024) .pdf
3. The instability of near-extreme Stokes waves (with S. Dyachenko, P. Lushnikov and A. Semenova), (submitted for publication, 2022) .pdf
4. Solving the heat equation with variable thermal conductivity (with M. Farkas), (submitted for publication, 2022) .pdf
5. 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

(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)