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)

(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. Numerical inverse scattering for the Korteweg-de Vries and modified Korteweg-de Vries equations (with Thomas Trogdon and Sheehan Olver) (Submitted for publication) .pdf.
2. Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation (with Vishal Vasan) (Submitted for publication) .pdf.
3. The instabilities of periodic traveling water waves with respect to transverse perturbations (with Katie Oliveras) (Submitted for publication) .pdf.
4. 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.

(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)