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)
- 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
- On the nonintegrability of equations for long- and short-wave interactions
(with J. Upsal, (submitted for publication, 2017)
The time-dependent Schrodinger equation with piecewise constant potentials (with N. Sheils), submitted for publication, 2017
The Stability Spectrum for Elliptic Solutions to the sine-Gordon equation
(with P. McGill and B. Segal) (Submitted for publication, 2017)
Fokas's Unified Transform Method for Linear Systems
(with Q. Guo, Eli Shlizerman and V. Vasan) (Submitted for publication, 2017)
The Stability Spectrum for Elliptic Solutions to the Focusing NLS
(with B. Segal) (Submitted for publication, 2016)
- 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.