{"id":28,"date":"2022-04-17T00:27:34","date_gmt":"2022-04-17T00:27:34","guid":{"rendered":"https:\/\/blogs.oregonstate.edu\/patnabelek\/?p=28"},"modified":"2022-04-26T18:06:57","modified_gmt":"2022-04-26T18:06:57","slug":"research","status":"publish","type":"post","link":"https:\/\/blogs.oregonstate.edu\/patnabelek\/2022\/04\/17\/research\/","title":{"rendered":"Publications and Manuscripts"},"content":{"rendered":"\n<p><strong>Publications:<\/strong><\/p>\n\n\n\n<p>7) Nabelek, P.V. &#8220;On solutions to the nonlocal dbar-problem and (2+1) dimensional completely integrable systems.&#8221; Lett Math Phys 111, 16 (2021).&nbsp;<a href=\"https:\/\/doi.org\/10.1007\/s11005-021-01353-w\">https:\/\/doi.org\/10.1007\/s11005-021-01353-w<\/a><\/p>\n\n\n\n<p>6) Nabelek, P.V. &#8220;Algebro-geometric finite gap solutions to the Korteweg\u2013de Vries equation as primitive solutions.&#8221; Phys D 414, 132709 (2020).&nbsp;<a href=\"https:\/\/doi.org\/10.1016\/j.physd.2020.132709\">https:\/\/doi.org\/10.1016\/j.physd.2020.132709<\/a><\/p>\n\n\n\n<p>5) Nabelek, P.V., Zakharov, V.E. &#8220;Solutions to the Kaup\u2013Broer system and its (2\uff0b1) dimensional integrable generalization via the dressing method.&#8221; Phys D 409, 132478 (2020).&nbsp;<a href=\"https:\/\/doi.org\/10.1016\/j.physd.2020.132478\">https:\/\/doi.org\/10.1016\/j.physd.2020.132478<\/a>.&nbsp;<\/p>\n\n\n\n<p>4) Dyachenko, S.A., Nabelek, P., Zakharov, D.V, Zakharov, V.E. &#8220;Primitive solutions of the Korteweg\u2013de Vries equation.&#8221; Theor Math Phys 202, 334\u2013343 (2020).&nbsp;<a href=\"https:\/\/doi.org\/10.1134\/S0040577920030058\">https:\/\/doi.org\/10.1134\/S0040577920030058<\/a><\/p>\n\n\n\n<p>3) McLaughlin, K.T-R, Nabelek, P.V. &#8220;A Riemann\u2013Hilbert Problem Approach to Infinite Gap Hill&#8217;s Operators and the Korteweg\u2013de Vries Equation.&#8221; Int Math Res Not 2, 1288\u20131352 (online 2019, print 2021).&nbsp;<a href=\"https:\/\/doi.org\/10.1093\/imrn\/rnz156\">https:\/\/doi.org\/10.1093\/imrn\/rnz156<\/a>.<\/p>\n\n\n\n<p>2) Nabelek, P., Zakharov, D., Zakharov, V. &#8220;On symmetric primitive potentials.&#8221; J Int Sys, 4:1, xyz006 (2019).&nbsp;<a href=\"https:\/\/doi.org\/10.1093\/integr\/xyz006\">https:\/\/doi.org\/10.1093\/integr\/xyz006<\/a><\/p>\n\n\n\n<p>1) Dissertation: Applications of Complex Variables to Spectral Theory and Completely Integrable Partial Differential Equations.\u00a0<a href=\"https:\/\/repository.arizona.edu\/handle\/10150\/627724\">https:\/\/repository.arizona.edu\/handle\/10150\/627724<\/a><\/p>\n\n\n\n<p><strong>Unpublished Manuscripts:<\/strong><\/p>\n\n\n\n<p>Nabelek, P., Pickrell, D. &#8220;Harmonic Maps and the Symplectic Category.&#8221; (2014) (arXiv:1404.2899)<\/p>\n\n\n\n<p>Nabelek, P. &#8220;Distributions Supported on Fractal Sets and Solutions to the Kadomtsev\u2013Petviashvili Equation.&#8221; (2020) (arXiv:2009.05864)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Publications: 7) Nabelek, P.V. &#8220;On solutions to the nonlocal dbar-problem and (2+1) dimensional completely integrable systems.&#8221; Lett Math Phys 111, 16 (2021).&nbsp;https:\/\/doi.org\/10.1007\/s11005-021-01353-w 6) Nabelek, P.V. &#8220;Algebro-geometric finite gap solutions to the Korteweg\u2013de Vries equation as primitive solutions.&#8221; Phys D 414, 132709 (2020).&nbsp;https:\/\/doi.org\/10.1016\/j.physd.2020.132709 5) Nabelek, P.V., Zakharov, V.E. &#8220;Solutions to the Kaup\u2013Broer system and its (2\uff0b1) [&hellip;]<\/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-28","post","type-post","status-publish","format-standard","hentry","category-information"],"_links":{"self":[{"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/posts\/28","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=28"}],"version-history":[{"count":13,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/posts\/28\/revisions"}],"predecessor-version":[{"id":84,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/posts\/28\/revisions\/84"}],"wp:attachment":[{"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/media?parent=28"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/categories?post=28"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/patnabelek\/wp-json\/wp\/v2\/tags?post=28"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}