Contact Info

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

M 10am-11am, W 2pm-3pm, Th 3pm-4pm via Zoom

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: 
Mathematical Physics, Nonlinear Waves, Riemann Surfaces, and Probability
Research Description: 

My research is on solitons, spinning things, donuts, and something random, sometimes on computers.

Publications:
1) Nabelek, P.V. "On solutions to the nonlocal dbar-problem and (2+1) dimensional completely integrable systems." Lett Math Phys 111, 16 (2021). https://doi.org/10.1007/s11005-021-01353-w

2) Nabelek, P.V. "Algebro-geometric finite gap solutions to the Korteweg–de Vries equation as primitive solutions." Phys D 414, 132709 (2020). https://doi.org/10.1016/j.physd.2020.132709

3) Nabelek, P.V., Zakharov, V.E. "Solutions to the Kaup–Broer system and its (2+1) dimensional integrable generalization via the dressing method." Phys D 409, 132478 (2020). https://doi.org/10.1016/j.physd.2020.132478.

4) Dyachenko, S.A., Nabelek, P., Zakharov, D.V, Zakharov, V.E. "Primitive solutions of the Korteweg–de Vries equation." Theor Math Phys 202, 334–343 (2020). https://doi.org/10.1134/S0040577920030058

5) McLaughlin, K.T-R, Nabelek, P.V. "A Riemann–Hilbert Problem Approach to Infinite Gap Hill's Operators and the Korteweg–de Vries Equation." Int Math Res Not 2, 1288–1352 (2021). https://doi.org/10.1093/imrn/rnz156.

6) Nabelek, P., Zakharov, D., Zakharov, V. "On symmetric primitive potentials." J Int Sys, 4:1, xyz006 (2019). https://doi.org/10.1093/integr/xyz006

Preprints:
Nabelek, P. "Distributions Supported on Fractal Sets and Solutions to the Kadomtsev--Petviashvili Equation." (2020) (arXiv:2009.05864)

Unpublished Manuscripts: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