{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T15:26:42Z","timestamp":1648567602675},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,10]]},"abstract":"<jats:p> In this paper, the generalized nonlinear Schr\u00f6dinger equation (GNLS) is studied. The bifurcation of solitary waves of the equation is discussed first, by using the bifurcation theory of planar dynamical systems. Then, the respective numbers of solitary waves are derived under different conditions on the equation parameters. Exact solutions of smooth solitary waves are obtained in the explicit form of a(\u03be)e<jats:sup>i(\u03c8(\u03be)-\u03c9t)<\/jats:sup>, \u03be = x - vt by qualitatively seeking the homoclinic and heteroclinic orbits for a class of Li\u00e9nard equations. Finally, nonsmooth solitary wave solutions of the GNLS are investigated. <\/jats:p>","DOI":"10.1142\/s0218127405013897","type":"journal-article","created":{"date-parts":[[2005,12,22]],"date-time":"2005-12-22T05:26:18Z","timestamp":1135229178000},"page":"3295-3305","source":"Crossref","is-referenced-by-count":4,"title":["BIFURCATION, EXACT SOLUTIONS AND NONSMOOTH BEHAVIOR OF SOLITARY WAVES IN THE GENERALIZED NONLINEAR SCHR\u00d6DINGER EQUATION"],"prefix":"10.1142","volume":"15","author":[{"given":"WEI","family":"WANG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIANHUA","family":"SUN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"GUANRONG","family":"CHEN","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, City University of Hong Kong, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Methods of Bifurcation Theory","author":"Chow S. N.","year":"1983"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/20\/8\/020"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/5\/2\/007"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.41.4478"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1063\/1.526113"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0307-904X(00)00031-7"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004425"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/33\/21\/307"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2003.07.027"},{"key":"rf11","first-page":"306","volume":"56","author":"Van Saarloos W.","journal-title":"Physica D"},{"key":"rf12","first-page":"281","volume":"27","author":"Wang W.","journal-title":"Acta Appl. Math. Sin."},{"key":"rf13","volume-title":"Introduction to Special Functions","author":"Wang Z. X.","year":"2000"},{"key":"rf14","first-page":"249","volume":"21","author":"Zhang W. G.","journal-title":"Acta Math. Appl. Sin."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405013897","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:09:04Z","timestamp":1565122144000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405013897"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,10]]},"references-count":14,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,10]]}},"alternative-id":["10.1142\/S0218127405013897"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405013897","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,10]]}}}