{"id":528,"date":"2023-11-24T07:37:03","date_gmt":"2023-11-24T10:37:03","guid":{"rendered":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/?p=528"},"modified":"2023-11-30T13:49:02","modified_gmt":"2023-11-30T16:49:02","slug":"stability-and-instability-for-the-fractional-kdv-equation-in-all-spatial-dimensions","status":"publish","type":"post","link":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/2023\/11\/stability-and-instability-for-the-fractional-kdv-equation-in-all-spatial-dimensions\/","title":{"rendered":"Stability and instability for the fractional KdV equation in all spatial dimensions"},"content":{"rendered":"<h3>Speaker: <span class=\"JtukPc\"><span id=\"rAECCd\" role=\"heading\" aria-level=\"1\"><a href=\"https:\/\/sites.google.com\/view\/oscar-riano-webpage\">Oscar Ria\u00f1o<\/a> <\/span><\/span><\/h3>\n<h3>Universidad Nacional de Colombia, Bogot\u00e1<\/h3>\n<h3>Date: Monday, November 27th, 2023 at 12 Santiago time<\/h3>\n<div>\n<p><strong>Abstract: <\/strong>We will study the fractional Korteweg-de Vries equation (fKdV) in several spatial dimensions. This is a nonlinear dispersive model where dispersive effects are studied through the fractional Laplacian. The equation appears in contexts such as water waves, waves in stratified fluids, boundary-layer type shear flow, and ion-acoustic waves, among others.<\/p>\n<div class=\"page\" title=\"Page 1\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>We will focus on traveling wave solutions (or solitary waves) of fKdV and analyze questions of orbital stability\/instability of such solutions. We will see that our results are valid for arbitrary dimen- sions, thus we recover and establish new results for the most studied case the one-dimensional fKdV.<\/p>\n<p>Joint work with Svetlana Roudenko (Florida International University (FIU)).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<p><strong>Venue:<\/strong>\u00a0 Sala de Seminarios, 5th floor, Beauchef 851 \/ <a href=\"https:\/\/reuna.zoom.us\/j\/81993551517?pwd=NkMyV2RtSThuY1JZaE5BN0s3ZFNOUT09\">Online via Zoom<\/a><br \/>\n<strong>Chair: <\/strong>Ricardo Freire<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Oscar Ria\u00f1o (Unal, Bogot\u00e1)<\/p>\n","protected":false},"author":85,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[5],"tags":[],"class_list":["post-528","post","type-post","status-publish","format-standard","hentry","category-past-seminar"],"_links":{"self":[{"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/528","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/users\/85"}],"replies":[{"embeddable":true,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/comments?post=528"}],"version-history":[{"count":1,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/528\/revisions"}],"predecessor-version":[{"id":529,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/posts\/528\/revisions\/529"}],"wp:attachment":[{"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/media?parent=528"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/categories?post=528"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/wp-json\/wp\/v2\/tags?post=528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}