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
- Numerical inverse scattering for the sine-Gordon equation
(with X. Yang and T. Trogdon), (submitted for publication, 2018)
- Stability of periodic traveling wave solutions to the Kawahara equation
(with O. Trichtchenko and R. Kollar, (submitted for publication, 2018)
- Direct Characterization of spectral stability of small amplitude periodic waves
in scalar problems via dispersion relation
(with R. Kollar and O. Trichtchenko, (submitted for publication, 2018)
- 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
- 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.