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)

(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. Real Lax Spectrum Implies Spectral Stability (with J. Upsal), (submitted for publication, 2019) .pdf.
2. The orbital stability of elliptic solutions of the Focusing Nonlinear Schrodinger Equation (with J. Upsal), (submitted for publication, 2019) .pdf.
3. Numerical inverse scattering for the sine-Gordon equation (with X. Yang and T. Trogdon), (submitted for publication, 2018) .pdf.
4. Stability of periodic traveling wave solutions to the Kawahara equation (with O. Trichtchenko and R. Kollar, (submitted for publication, 2018) .pdf.
5. 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) .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)