{"id":1259,"date":"2025-02-23T11:13:45","date_gmt":"2025-02-23T19:13:45","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1259"},"modified":"2025-05-04T19:35:34","modified_gmt":"2025-05-05T02:35:34","slug":"dispersive-quantisation-in-kdv","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/02\/23\/dispersive-quantisation-in-kdv\/","title":{"rendered":"Dispersive quantisation in KdV"},"content":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0<strong>February<\/strong><strong> 25<\/strong><strong>th<\/strong>, will be at\u00a0<strong>3<\/strong><strong>:30pm<\/strong>\u00a0in\u00a0<strong>Room 740.<\/strong><\/p>\n<p><strong>Speaker:\u00a0<\/strong>Jason Zhao<\/p>\n<p><strong>Abstract:\u00a0<\/strong>It has been observed both experimentally and mathematically that solutions to linear dispersive equations, such as the Schrodinger and Airy equations, posed on the torus exhibit dramatically different behaviors between rational and irrational times. For example, the evolution of piecewise constant data remains so at rational times, while it becomes continuous and fractalised at irrational times. A natural question to ask is whether this<em> Talbot effect<\/em>, as it broadly known, persists under non-linear dispersive flows. Focusing on the KdV equation, we will present two perspectives which follow in the spirit of the seminal works of Bourgain (1993) and Babin-Ilyin-Titi (2011): the first is the non-linear smoothing effect observed by Erdogan-Tzirakis (2013), and the second is the numerical work of Hofmanova-Schratz (2017) and Rousset-Schratz (2022}.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0February 25th, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Jason Zhao Abstract:\u00a0It has been observed both experimentally and mathematically that solutions to linear dispersive equations, such as the Schrodinger and Airy equations, posed on the torus exhibit dramatically different behaviors between rational and irrational times. For example, the evolution of piecewise constant data remains [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,1],"tags":[],"class_list":["post-1259","post","type-post","status-publish","format-standard","hentry","category-spring-2025","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1259","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1259"}],"version-history":[{"count":2,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1259\/revisions"}],"predecessor-version":[{"id":1262,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1259\/revisions\/1262"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1259"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1259"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}