Michael A. Nivala (2009, UCLA Postdoc)
Katie Oliveras (2009, Seattle U. Instructor)
Chris Curtis (2009, U. of Colorado Postdoc)
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.
- Stability of gravity waves in the presence of surface tension (with O. Trichtchenko) (Submitted for publication, 2013) .pdf.
- Non-steady state heat conduction in composite walls (with B. Pelloni and N. E. Sheils) (Submitted for publication, 2013) .pdf.
- 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.
- Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: computational results (with Tom Trogdon) (Submitted for publication, 2013) .pdf.
- A numerical dressing method for the nonlinear superposition of solutions of the KdV equation (with Tom Trogdon) (Submitted for publication, 2013).pdf.
- Riemann Constant Vector. Maple software for the computation of the Riemann Constant Vector of a Riemann surface specified as a plane algebraic curve.
- SpectrUW 2.0:Freeware for the computation of spectra of linear operators.