{"id":39,"date":"2022-04-26T00:46:52","date_gmt":"2022-04-26T00:46:52","guid":{"rendered":"https:\/\/blogs.oregonstate.edu\/patnabelek\/?p=39"},"modified":"2022-05-14T00:56:48","modified_gmt":"2022-05-14T00:56:48","slug":"contact-information","status":"publish","type":"post","link":"https:\/\/blogs.oregonstate.edu\/patnabelek\/2022\/04\/26\/contact-information\/","title":{"rendered":"About Me"},"content":{"rendered":"\n

My name is Patrik Nabelek, and this is my personal webpage. My research is on mathematical physics generally, and on nonlinear differential equations describing wave motion with a focus on the formation and replication of hydrodynamic soliton gasses in shallow water. I am also interested in nonlinear electromagnetic waves and soliton gas formation within fiber optic cables. I am interested in completely integrable Hamiltonian systems, translation surfaces, and donuts. I am also interested in probability and statistical models in classical linear and nonlinear wave mechanics. If you would like to contact me, please send me an email at nabelekp@oregonstate.edu<\/a>.<\/p>\n\n\n\n

In my research, I use methods from functional analysis, complex analysis, spectral theory, and geometry. I am also interested in the use finite difference methods and psuedo-spectral methods to solve problems relevant in ocean engineering and nonlinear optics. One of my focuses is on completely integrable systems that describe phenomena in classical, quantum, and wave mechanics.<\/p>\n\n\n\n

I am also interested in real and complex manifolds and surfaces from the points of view of both algebraic and Riemannian geometry. I focus on Riemann surfaces, and their complex structures, translation structures, flat cone metrics metrics, and their harmonic maps into semi-simple Lie groups. But I am also interested in holomorphic and meromorphic functions on two dimensional complex manifolds. I study these topics in connection with the theory of completely integrable Hamiltonian systems in finite and infinite dimensions, and on the study of soliton gasses.<\/p>\n\n\n\n

I am particularly interested in: the Korteweg–de Vries equation, the one dimensional Boussinesq equation, and Kaup–Broer system for shallow water; the cubic nonlinear Schrodinger equation for deep water waves; the Burgers equation for gas dynamics. I am also interested in the Hamiltonian formulation of the deep and shallow water wave wave systems, and the complete integrability conjecture for one dimensional deep water wave system.<\/p>\n\n\n\n

I currently work as a postdoc at Oregon State University teaching classes on these subjects senior level mathematics undergraduate students and masters level engineering graduate students. I received a PhD in Applied Mathematics from UA in 2018 working under Vladimir Zakharov and Ken McLaughlin, and a BS in Mathematics from Oregon State University.<\/p>\n\n\n\n

Webpages I Like: ONR: Atlas of Internal Waves<\/a>, SIAM<\/a>, AMS<\/a>, NOAA (Ocean and Coasts)<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

My name is Patrik Nabelek, and this is my personal webpage. My research is on mathematical physics generally, and on nonlinear differential equations describing wave motion with a focus on the formation and replication of hydrodynamic soliton gasses in shallow water. I am also interested in nonlinear electromagnetic waves and soliton gas formation within fiber […]<\/p>\n","protected":false},"author":10272,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-39","post","type-post","status-publish","format-standard","hentry","category-information"],"_links":{"self":[{"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/posts\/39","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/users\/10272"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/comments?post=39"}],"version-history":[{"count":20,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/posts\/39\/revisions"}],"predecessor-version":[{"id":110,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/posts\/39\/revisions\/110"}],"wp:attachment":[{"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/media?parent=39"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/categories?post=39"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/tags?post=39"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}