Bernard Deconinck’s Research

Research topics

Polar plot of an eigenfunction for a spectral problem

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

  1. Stability of gravity waves in the presence of surface tension (with O. Trichtchenko) (Submitted for publication, 2013) .pdf.
  2. Non-steady state heat conduction in composite walls (with B. Pelloni and N. E. Sheils) (Submitted for publication, 2013) .pdf.
  3. Short-wave transverse instabilities of line solitons of the 2-D hyperbolic nonlinear Schrodinger equation (with D. E. Pelinovsky, E. A. Ruvinsakaya and O. A. Kurkina) (Submitted for publication, 2013) .pdf.
  4. Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: computational results (with Tom Trogdon) (Submitted for publication, 2013) .pdf.
  5. A numerical dressing method for the nonlinear superposition of solutions of the KdV equation (with Tom Trogdon) (Submitted for publication, 2013).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)