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.

PhD in Applied Mathematics, University of Arizona, 2018

MS in Applied Mathematics, University of Arizona, 2015

BS in Mathematics, Oregon State University, 2012

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Unpublished Manuscripts: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

Classes: