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
- The Stability Spectrum for Elliptic Solutions to the sine-Gordon equation Equation (with P. McGill and B. Segal) (Submitted for publication, 2017).
- Fokas's Unified Transform Method for Linear Systems (with Q. Guo, Eli Shlizerman and V. Vasan) (Submitted for publication, 2017).
- The Stability Spectrum for Elliptic Solutions to the Focusing NLS Equation (with B. Segal) (Submitted for publication, 2016).
- Explicit solutions for a long-wave model with constant vorticity (with B. Segal, D. Moldabayev and H. Kalisch ) (Submitted for publication, 2016).
- The interaction of long and short waves in dispersive media (with N. Nguyen and B. Segal ) Journal of Physics A, 415501, 2016.
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.