{"id":2108,"date":"2021-01-12T10:05:23","date_gmt":"2021-01-12T18:05:23","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=2108"},"modified":"2021-03-17T14:12:01","modified_gmt":"2021-03-17T21:12:01","slug":"applied-math-talk-periodic-travelling-waves-in-nonlinear-wave-equations-modulation-instability-and-rogue-waves-by-dmitry-pelinovsky-mcmaster-university-canada","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/applied-math-talk-periodic-travelling-waves-in-nonlinear-wave-equations-modulation-instability-and-rogue-waves-by-dmitry-pelinovsky-mcmaster-university-canada\/","title":{"rendered":"Applied math. talk: Periodic travelling waves in nonlinear wave equations: modulation instability and rogue waves by Dmitry Pelinovsky, McMaster University, Canada"},"content":{"rendered":"

Abstract: \u00a0 \u00a0 I will overview the following different wave phenomena in
\nintegrable nonlinear wave equations:<\/p>\n

(1) universal patterns in the dynamics of fluxon condensates in the
\nsemi-classical limit;
\n(2) modulational instability of periodic travelling waves;
\n(3) rogue waves on the background of periodic and double-periodic waves.<\/p>\n

Main examples include the sine-Gordon equation, the nonlinear
\nSchroedinger equation, and the derivative nonlinear Schroedinger
\nequation. For the latter equation, in collaboration with Jinbing Chen
\n(South East University, China) and Jeremy Upsal (University of
\nWashington, USA), we adapted the method of nonlinearization of the Lax
\nsystem in order to characterize the existence and modulation stability
\nof periodic travelling waves. We give precise information on the
\nlocation of Lax and stability spectra, with assistance of numerical
\npackage based on the so-called Hill’s method. Particularly interesting
\noutcome is the explicit relation between the onset of modulation
\ninstability and the existence of a rogue wave (localized solution in
\nspace and time) on the background of periodic travelling waves.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Abstract: \u00a0 \u00a0 I will overview the following different wave phenomena in integrable nonlinear wave equations: (1) universal patterns in the dynamics of fluxon condensates in the semi-classical limit; (2) […]<\/p>\n","protected":false},"author":162,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[15],"class_list":["post-2108","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-applied-math-seminar","cat_applied-math-seminar"],"acf":[],"yoast_head":"\nApplied math. talk: Periodic travelling waves in nonlinear wave equations: modulation instability and rogue waves by Dmitry Pelinovsky, McMaster University, Canada - Claremont Center for the Mathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/colleges.claremont.edu\/ccms\/event\/applied-math-talk-periodic-travelling-waves-in-nonlinear-wave-equations-modulation-instability-and-rogue-waves-by-dmitry-pelinovsky-mcmaster-university-canada\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Applied math. talk: Periodic travelling waves in nonlinear wave equations: modulation instability and rogue waves by Dmitry Pelinovsky, McMaster University, Canada - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Abstract: \u00a0 \u00a0 I will overview the following different wave phenomena in integrable nonlinear wave equations: (1) universal patterns in the dynamics of fluxon condensates in the semi-classical limit; 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