Applied Mathematics - University of Washington

AMATH University             
          of Washington

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
Natalie Sheils (2015, Postdoc at U. of Minnesota)
Olga Trichtchenko (2014, Postdoc at UCL, London)
Thomas Trogdon (2013, NSF Postdoc at NYU)
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 Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation (with B. Segal) (Submitted for publication, 2016) .pdf.
  2. Explicit solutions for a long-wave model with constant vorticity (with B. Segal, D. Moldabayev and H. Kalisch ) (Submitted for publication, 2016) .pdf.
  3. The interaction of long and short waves in dispersive media (with N. Nguyen and B. Segal ) Journal of Physics A, 415501, 2016 .pdf.
  4. The instability of Wilton ripples (with O. Trichtchenko and J. Wilkening) (Submitted for publication, 2015) .pdf.
  5. The linear KdV equation with an interface (with N. E. Sheils and D. A. Smith) (Submitted for publication, 2015) .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)
Department of Applied Mathematics, University of Washington, Lewis Hall #202, Box 353925, Seattle, WA 98195-3925 USA
Email 'info' (at Phone 206-543-5493 Fax 206-685-1440