Contact Info

Primary Title: 
Postdoctoral Scholar
Email Contact: 
Office: 
KIDD 008
Bio: 

Patrik was an undergraduate at Oregon State University, and received his BS in Mathematics. Patrik received his PhD in Applied Mathematics from the University of Arizona working under the supervision of Ken McLaughlin and Vladimir Zakharov.

Education

PhD in Applied Mathematics, University of Arizona, 2018
MS in Applied Mathematics, University of Arizona, 2015
BS in Mathematics, Oregon State University, 2012

Research

Research Field: 
Linear and Nonlinear Waves, Physics, Geometry, Differential Equations, Probability, and Numerical Analysis
Research Description: 

Solitons, spinning things, donuts, and something random on computers.

Publications:
(2020) P. Nabelek. "Algebro-Geometric Finite Gap Solutions to the Korteweg–de Vries Equation as Primitive Solutions." Phys. D.
(2020) P. Nabelek, V. Zakharov. "Solutions to the Kaup–Broer system and its (2+1) dimensional integrable generalization via the dressing method." Phys. D.
(2020) S. Dyachenko, P. Nabelek, D. Zakharov, V. Zakharov. "Primitive Solutions to the Korteweg de--Vreis Equation." TMP.
(2019) K. McLaughlin, P. Nabelek. "A Riemann–Hilbert Problem Approach to Infinite Gap Hill’s Operators and the Korteweg–de Vries Equation." IMRN.
(2019) P. Nabelek, D. Zakharov, V. Zakharov. "On Symmetric Primitive Potentials." J. Int. Sys.

Preprints:
(2020) P. Nabelek. "Cantor and Sierpinski Surfaces as Spectral Curves for Solutions to the Kadomtsev--Petviashvili Equation." (arXiv:2009.05864)
(2020) P. Nabelek. "On Solutions to the Nonlocal Dbar Problem and (2+1) Dimensional Completely Integrable Systems." (arXiv:2008.13237)

Unpublished Manuscripts:
(2014) P. Nabelek, D. Pickrell. ``Harmonic Maps and the Symplectic Category.'' (arXiv:1404.2899)

Talks (PDF Slides):
OSU REU Colloquium 2020
SIAM PNW 2019
Analysis Seminar 2019
OSU REU Colloquium 2019
OSU CAM Seminar 2018
Dissertation Defense 2017