{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:46:56Z","timestamp":1772293616841,"version":"3.50.1"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2011,2]]},"abstract":"<jats:p> For the Lax KdV5 equation and the KdV\u2013Sawada\u2013Kotera\u2013Ramani equation, their corresponding four-dimensional traveling wave systems are studied by using Congrove's method. Exact explicit gap soliton, embedded soliton, periodic and quasi-periodic wave solutions are obtained. The existence of homoclinic manifolds to three kinds of equilibria including a hyperbolic equilibrium, a center-saddle and an equilibrium with zero pair of eigenvalues is revealed. The bifurcation conditions of equilibria are given. <\/jats:p>","DOI":"10.1142\/s0218127411028581","type":"journal-article","created":{"date-parts":[[2011,3,10]],"date-time":"2011-03-10T10:07:52Z","timestamp":1299751672000},"page":"527-543","source":"Crossref","is-referenced-by-count":11,"title":["HOMOCLINIC MANIFOLDS, CENTER MANIFOLDS AND EXACT SOLUTIONS OF FOUR-DIMENSIONAL TRAVELING WAVE SYSTEMS FOR TWO CLASSES OF NONLINEAR WAVE EQUATIONS"],"prefix":"10.1142","volume":"21","author":[{"given":"JIBIN","family":"LI","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"},{"name":"Department of Mathematics, Kunming University of Science, and Technology, Kunming, Yunnan 650093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YI","family":"ZHANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(00)00355-8"},{"key":"rf2","first-page":"340","volume":"153","author":"Champneys A. R.","journal-title":"Physica D"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2008.01.005"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9590.00130"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2009.11.071"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.52.744"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1063\/1.2953474"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.61.51"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.2991\/jnmp.2001.8.3.4"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160210503"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.02.047"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.08.007"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2006.01.009"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9590.00169"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(01)00327-5"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127411028581","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:56:46Z","timestamp":1565189806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127411028581"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2]]},"references-count":15,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2011,2]]}},"alternative-id":["10.1142\/S0218127411028581"],"URL":"https:\/\/doi.org\/10.1142\/s0218127411028581","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2]]}}}