{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T02:24:03Z","timestamp":1649211843166},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2016,3,21]],"date-time":"2016-03-21T00:00:00Z","timestamp":1458518400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[2016,6]]},"abstract":"<jats:p>We prove the existence of solitary wave solutions to the quasilinear Benney system<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0308210515000578_equ01\" \/><\/jats:disp-formula><\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0308210515000578_equ02\" \/><\/jats:disp-formula><\/jats:p><jats:p>where <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0308210515000578_inline01\" \/>, \u20131 &lt; <jats:italic>p<\/jats:italic> &lt; +\u221e and <jats:italic>a<\/jats:italic>, \u03b3 &gt; 0. We establish, in particular, the existence of travelling waves with speed arbitrarily large if <jats:italic>p<\/jats:italic> &lt; 0 and arbitrarily close to 0 if <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0308210515000578_inline02\" \/>. We also show the existence of standing waves in the case <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0308210515000578_inline03\" \/>, with compact support if \u2013 1 &lt; <jats:italic>p<\/jats:italic> &lt; 0. Finally, we obtain, under certain conditions, the linearized stability of such solutions.<\/jats:p>","DOI":"10.1017\/s0308210515000578","type":"journal-article","created":{"date-parts":[[2016,3,21]],"date-time":"2016-03-21T05:08:17Z","timestamp":1458536897000},"page":"547-564","source":"Crossref","is-referenced-by-count":2,"title":["Existence and linearized stability of solitary waves for a quasilinear Benney system"],"prefix":"10.1017","volume":"146","author":[{"given":"Jo\u00e3o-Paulo","family":"Dias","sequence":"first","affiliation":[]},{"given":"M\u00e1rio","family":"Figueira","sequence":"additional","affiliation":[]},{"given":"Filipe","family":"Oliveira","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,3,21]]},"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210515000578","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T23:15:21Z","timestamp":1555629321000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210515000578\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,21]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["S0308210515000578"],"URL":"https:\/\/doi.org\/10.1017\/s0308210515000578","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,21]]}}}