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