Publications:
7) 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
6) 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
5) 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
3) 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 (online 2019, print 2021). https://doi.org/10.1093/imrn/rnz156.
2) Nabelek, P., Zakharov, D., Zakharov, V. “On symmetric primitive potentials.” J Int Sys, 4:1, xyz006 (2019). https://doi.org/10.1093/integr/xyz006
1) Dissertation: Applications of Complex Variables to Spectral Theory and Completely Integrable Partial Differential Equations. https://repository.arizona.edu/handle/10150/627724
Unpublished Manuscripts:
Nabelek, P., Pickrell, D. “Harmonic Maps and the Symplectic Category.” (2014) (arXiv:1404.2899)
Nabelek, P. “Distributions Supported on Fractal Sets and Solutions to the Kadomtsev–Petviashvili Equation.” (2020) (arXiv:2009.05864)
