{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T14:41:21Z","timestamp":1771339281157,"version":"3.50.1"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p> In this paper, we apply the method of dynamical systems to a generalized two-component Camassa\u2013Holm system. Through analysis, we obtain solitary wave solutions, kink and anti-kink wave solutions, cusp wave solutions, breaking wave solutions, and smooth and nonsmooth periodic wave solutions. To guarantee the existence of these solutions, we give constraint conditions among the parameters associated with the generalized Camassa\u2013Holm system. Choosing some special parameters, we obtain exact parametric representations of the traveling wave solutions. <\/jats:p>","DOI":"10.1142\/s0218127412503051","type":"journal-article","created":{"date-parts":[[2013,1,15]],"date-time":"2013-01-15T06:54:47Z","timestamp":1358232887000},"page":"1250305","source":"Crossref","is-referenced-by-count":26,"title":["BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED TWO-COMPONENT CAMASSA\u2013HOLM EQUATION"],"prefix":"10.1142","volume":"22","author":[{"given":"JIBIN","family":"LI","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZHIJUN","family":"QIAO","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Texas Pan-American, 1201 West University Drive, Edinburg, TX 78541, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,1,14]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65138-0"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.71.1661"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-2156(08)70254-0"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-005-0041-7"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2011.556695"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406016033"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407019858"},{"key":"rf8","volume-title":"On the Study of Singular Nonlinear Travelling Wave Equations: Dynamical Approach","author":"Li J.","year":"2007"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-008-6207-3"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410025582"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1063\/1.3385777"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.53.1900"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/94\/50003"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i2005-10453-y"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412503051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:25:48Z","timestamp":1565133948000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412503051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":14,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2013,1,14]]},"published-print":{"date-parts":[[2012,12]]}},"alternative-id":["10.1142\/S0218127412503051"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412503051","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}