{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:34Z","timestamp":1740134554600,"version":"3.37.3"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11071164","13ZZ118","XTKX2012"],"award-info":[{"award-number":["11071164","13ZZ118","XTKX2012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovation Program of Shanghai Municipal Education Commission","award":["11071164","13ZZ118","XTKX2012"],"award-info":[{"award-number":["11071164","13ZZ118","XTKX2012"]}]},{"DOI":"10.13039\/501100012150","name":"Shanghai Leading Academic Discipline Project","doi-asserted-by":"crossref","award":["11071164","13ZZ118","XTKX2012"],"award-info":[{"award-number":["11071164","13ZZ118","XTKX2012"]}],"id":[{"id":"10.13039\/501100012150","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>This paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. Since<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>J<\/mml:mi><\/mml:mrow><\/mml:math>is not onto, Grillakis-Shatah-Strauss theory cannot be applied on the system directly. We overcome this difficulty and obtain the general conclusion on orbital stability of solitary waves in this paper. Then, according to two exact solitary waves of the equations, we deduce the explicit expression of discrimination<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msup><mml:mrow><mml:mi>d<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u2032<\/mml:mi><mml:mi>\u2032<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>and give several sufficient conditions which can be used to judge the orbital stability and instability for the two solitary waves. Furthermore, we analyze the influence of the interaction between two nonlinear terms of the equations on the wave speed interval which makes the solitary waves stable.<\/jats:p>","DOI":"10.1155\/2014\/963987","type":"journal-article","created":{"date-parts":[[2014,5,26]],"date-time":"2014-05-26T21:06:35Z","timestamp":1401138395000},"page":"1-16","source":"Crossref","is-referenced-by-count":0,"title":["Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6853-1287","authenticated-orcid":true,"given":"Weiguo","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8258-0701","authenticated-orcid":true,"given":"Xu","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5094-0602","authenticated-orcid":true,"given":"Zhengming","family":"Li","sequence":"additional","affiliation":[{"name":"Business School, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiyan","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"issue":"1","key":"1","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1063\/1.864487","volume":"27","year":"1984","journal-title":"Physics of Fluids"},{"issue":"3","key":"2","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0010-4655(77)90009-1","volume":"13","year":"1977","journal-title":"Computer Physics Communications"},{"issue":"4","key":"3","first-page":"297","volume":"5","year":"1987","journal-title":"Journal of Computational Mathematics"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02006073"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02013752"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1088\/1009-1963\/12\/2\/304"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(97)00325-4"},{"key":"8"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(87)90044-9"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(90)90016-E"},{"year":"1993","key":"12","first-page":"xiv+695"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01053535"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1987.0073"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/963987.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/963987.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/963987.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,11]],"date-time":"2020-05-11T23:50:45Z","timestamp":1589241045000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/963987\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":14,"alternative-id":["963987","963987"],"URL":"https:\/\/doi.org\/10.1155\/2014\/963987","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}