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
- Michael A. Nivala (2009, UCLA Postdoc)
- Katie Oliveras (2009, Seattle U. Instructor)
- Chris Curtis (2009, U. of Colorado Postdoc)
- 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 Korteweg-de Vries and modified Korteweg-de Vries equations (with Thomas Trogdon and Sheehan Olver) (Submitted for publication) .pdf.
- Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation (with Vishal Vasan) (Submitted for publication)
- The instabilities of periodic traveling water waves with respect to transverse perturbations
(with Katie Oliveras) (Submitted for publication) .pdf.
- Recovering the water-wave surface from pressure measurements
(with Diane Henderson, Katie Oliveras, and Vishal Vasan)
(Accepted for the 10th International Conference on Mathematical and
Numerical Aspects of Waves (Refereed Proceedings), WAVES 2011,
Vancouver July 25-29, 2011) .pdf.
- 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.