{"id":7902,"date":"2024-09-13T11:32:04","date_gmt":"2024-09-13T08:32:04","guid":{"rendered":"https:\/\/quantum-electronics.ru\/en\/?p=7902"},"modified":"2024-09-13T13:47:12","modified_gmt":"2024-09-13T10:47:12","slug":"fast-numerical-method-of-the-second-order-of-accuracy-for-solving-the-inverse-scattering-problem","status":"publish","type":"post","link":"https:\/\/quantum-electronics.ru\/en\/fast-numerical-method-of-the-second-order-of-accuracy-for-solving-the-inverse-scattering-problem\/","title":{"rendered":"Fast numerical method of the second order of accuracy for solving the inverse scattering problem"},"content":{"rendered":"<p>O. V. Belai<\/p>\n<ul>\n<li>Institute of Automation and Electrometry, Siberian Branch of Russian Academy of Sciences, Novosibirsk<\/li>\n<\/ul>\n<div class=\"around-button\"><b>Abstract:<\/b> A method is proposed for the numerical solution of the inverse scattering problem formulated in the form of integral equations of the Gelfand\u2013Levitan\u2013Marchenko type. Approximation of integral equations is performed with the second order of accuracy, which leads to a system of equations with a non-Toeplitz matrix; however, the method requires <i>O<\/i>(<i>N<\/i><sup>2<\/sup>) arithmetic operations. The method is applied to the problem of self-focusing of radiation with allowance for polarisation, which was solved by Manakov.<\/div>\n<div><\/div>\n<div class=\"around-button\"><b>Keywords:<\/b> inverse scattering problem, Toeplitz matrix, soliton, Manakov system<\/div>\n<div><\/div>\n<div><b>Received:<\/b> 16.09.2022<br \/>\n<b>Revised:<\/b> 31.10.2022<br \/>\n<b>Accepted:<\/b> 31.10.2022<\/div>\n<div><\/div>\n<div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>O. V. Belai Institute of Automation and Electrometry, Siberian Branch of Russian Academy of Sciences, Novosibirsk Abstract: A method is proposed for the numerical solution of the inverse scattering problem formulated in the form of integral equations of the Gelfand\u2013Levitan\u2013Marchenko type. Approximation of integral equations is performed with the second order of accuracy, which leads\u2026 <span class=\"read-more\"><a href=\"https:\/\/quantum-electronics.ru\/en\/fast-numerical-method-of-the-second-order-of-accuracy-for-solving-the-inverse-scattering-problem\/\">Read More &raquo;<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[3084],"class_list":["post-7902","post","type-post","status-publish","format-standard","hentry","category-stats","tag-o-v-belai"],"_links":{"self":[{"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/posts\/7902","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/comments?post=7902"}],"version-history":[{"count":0,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/posts\/7902\/revisions"}],"wp:attachment":[{"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/media?parent=7902"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/categories?post=7902"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/quantum-electronics.ru\/en\/wp-json\/wp\/v2\/tags?post=7902"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}