{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:47:08Z","timestamp":1777448828827,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2010,8,1]],"date-time":"2010-08-01T00:00:00Z","timestamp":1280620800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2010,8]]},"abstract":"<jats:p>We develop a microlocal study for scalar classical analytic pseudo-differential operators of principal type. Next, we reduce a system of pseudo-differential operators to the normal form. Then we obtain asymptotic expansion and the exact exponential decay rate for the width of resonances arising from microlocal tunneling effect.<\/jats:p>","DOI":"10.3233\/asy-2010-0993","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:12:37Z","timestamp":1575054757000},"page":"1-29","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotic expansion for the widths of resonances in Born\u2013Oppenheimer approximation"],"prefix":"10.1177","volume":"69","author":[{"given":"Hamadi","family":"Baklouti","sequence":"first","affiliation":[{"name":"D\u00e9partement de math\u00e9matiques, Facult\u00e9 des sciences de Sfax, Route de soukra Km 3.5, B. P. 1171, 3000, Sfax, Tunisie. E-mail: h.baklouti@gmail.com"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2010,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-0993","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-0993","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:06Z","timestamp":1777379946000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2010-0993"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2010,8]]}},"alternative-id":["10.3233\/ASY-2010-0993"],"URL":"https:\/\/doi.org\/10.3233\/asy-2010-0993","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8]]}}}