{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T04:59:04Z","timestamp":1775365144529,"version":"3.50.1"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006570","name":"Coordinaci\u00f3n de la Investigaci\u00f3n Cient\u00edfica","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006570","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University of Cartagena"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2007]]},"abstract":"<jats:p>As is well known, submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E1\"><mml:mi>k<\/mml:mi><\/mml:math>in the direction of the cylinders, there is only one trapped wave. We construct asymptotics of these trapped modes and their frequencies as<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"E2\"><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>\u2192<\/mml:mo><mml:mi>\u221e<\/mml:mi><\/mml:mrow><\/mml:math>in the case of one or two submerged cylinders by means of reducing the initial problem to a system of integral equations on the boundaries and then solving them using a technique suggested by Zhevandrov and Merzon (2003).<\/jats:p>","DOI":"10.1155\/2007\/80205","type":"journal-article","created":{"date-parts":[[2007,9,19]],"date-time":"2007-09-19T06:04:49Z","timestamp":1190181889000},"page":"1-17","source":"Crossref","is-referenced-by-count":4,"title":["Waves Trapped by Submerged Obstacles at High Frequencies"],"prefix":"10.1155","volume":"2007","author":[{"given":"A. M.","family":"Mar\u00edn","sequence":"first","affiliation":[]},{"given":"R. D.","family":"Ort\u00edz","sequence":"additional","affiliation":[]},{"given":"P.","family":"Zhevandrov","sequence":"additional","affiliation":[]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1017\/S0305004100026700","volume":"47","year":"1951","journal-title":"Mathematical Proceedings of the Cambridge Philosophical Society"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1137\/0153071"},{"key":"3","first-page":"xviii+513","year":"2002"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.01.043"},{"key":"5","series-title":"Amer. Math. Soc. Transl. Ser. 2","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1090\/trans2\/208\/04","volume-title":"Asymptotics of eigenfunctions in shallow potential wells and related problems","volume":"208","year":"2003"},{"key":"6","series-title":"Addison-Wesley Series in Advanced Physics","first-page":"xii+515","year":"1958"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(76)90038-5"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019615509634"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010441313887"},{"key":"10","year":"1970"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2007\/080205.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2007\/080205.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,17]],"date-time":"2017-06-17T19:08:33Z","timestamp":1497726513000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2007\/080205\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"references-count":10,"alternative-id":["080205","80205"],"URL":"https:\/\/doi.org\/10.1155\/2007\/80205","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007]]}}}