{"id":5067,"date":"2023-03-16T05:06:02","date_gmt":"2023-03-16T05:06:02","guid":{"rendered":"https:\/\/iamm.in.ua\/?p=5067"},"modified":"2023-03-29T07:57:43","modified_gmt":"2023-03-29T07:57:43","slug":"seminar-contemporary-analysis-and-partial-differential-equations-23-03-2023","status":"publish","type":"post","link":"https:\/\/iamm.in.ua\/?p=5067&lang=en","title":{"rendered":"SEMINAR \u201cContemporary Analysis and Partial Differential Equations\u201d (23.03.2023)"},"content":{"rendered":"<p><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><img decoding=\"async\" loading=\"lazy\" class=\"size-medium wp-image-4770 alignright\" src=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea-300x84.jpg\" alt=\"\" width=\"300\" height=\"84\" srcset=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea-300x84.jpg 300w, https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Allea.jpg 483w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-4773 alignleft\" src=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM-300x292.png\" alt=\"\" width=\"133\" height=\"129\" srcset=\"https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM-300x292.png 300w, https:\/\/iamm.in.ua\/wp-content\/uploads\/2023\/01\/Logo-IAMM.png 583w\" sizes=\"(max-width: 133px) 100vw, 133px\" \/><\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/scholar.google.com\/citations?hl=en&amp;user=4qKopsUAAAAJ&amp;view_op=list_works&amp;sortby=pubdate\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong>Eugene Benilov<\/strong><\/span><\/a><\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 14pt; font-family: georgia, palatino, serif;\">University of Limerick, Ireland<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-size: 14pt; font-family: georgia, palatino, serif;\">eugene.benilov@ul.ie<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong><em>Solitary and Periodic Waves in a Fifth-Order Korteweg-de Vries Equation<\/em><\/strong><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Thursday, 23 March 2023 at 15:00<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">On line:&nbsp;<a href=\"http:\/\/meet.google.com\/nif-zfwd-mrg\" target=\"_blank\" rel=\"noopener\">http:\/\/meet.google.com\/nif-zfwd-mrg<\/a><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><strong>Abstract<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">I consider a fifth-order KdV equation, where the fifth-order derivative term is multiplied by a small parameter \u03b5. It has been conjectured that this equation admits a non-local solitary wave solution which has a central core and an oscillatory tail either behind or in front of the core. I shall prove that this solution cannot be exactly steady; instead, the amplitude of the central core decays due to the energy flux generated in the oscillatory tail. The decay rate is calculated in the limit <span style=\"font-family: 'times new roman', times, serif;\">\u03b5 \u2192 0<\/span>. In order to verify the analytical results, I have developed a high-precision spectral method for numerical integration of this equation. The asymptotic and numerical result show good agreement.<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\">Seminar video report <\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; font-size: 14pt;\"><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/csgHp6Tx0-4\" width=\"560\" height=\"314\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"slide-text-bg2\"><span>&nbsp; &nbsp; &nbsp; &nbsp; Eugene Benilov University of Limerick, Ireland eugene.benilov@ul.ie Solitary and Periodic Waves in a Fifth-Order Korteweg-de Vr<\/span><\/div>\n<div class=\"slide-btn-area-sm\"><a href=\"https:\/\/iamm.in.ua\/?p=5067&#038;lang=en\" class=\"slide-btn-sm\">\u041f\u0440\u043e\u0447\u0438\u0442\u0430\u0442\u044c \u0431\u043e\u043b\u044c\u0448\u0435<\/a><\/div>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[99,74],"tags":[],"_links":{"self":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5067"}],"collection":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5067"}],"version-history":[{"count":7,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5067\/revisions"}],"predecessor-version":[{"id":5146,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=\/wp\/v2\/posts\/5067\/revisions\/5146"}],"wp:attachment":[{"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5067"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5067"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iamm.in.ua\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5067"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}