{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T19:38:10Z","timestamp":1783107490265,"version":"3.54.6"},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,4]]},"abstract":"<jats:p> A model of dynamics of protons in hydrogen-bonded quasi-one-dimensional networks was derived, which is a singular system of the second kind with three parameters and two singular straight lines. In this paper, we use the method of dynamical systems to discuss the bifurcations of phase portraits of the vector fields defined by the singular system. Corresponding to the phase orbits of the system in different parameter conditions, we compute all possible exact parametric representations of solutions. It is shown that in given parameter conditions, there exist solitary wave solutions, kink wave solutions and periodic wave solutions. The mentioned system has no peakon solution. <\/jats:p>","DOI":"10.1142\/s0218127415500625","type":"journal-article","created":{"date-parts":[[2015,5,4]],"date-time":"2015-05-04T06:52:15Z","timestamp":1430722335000},"page":"1550062","source":"Crossref","is-referenced-by-count":7,"title":["Bifurcations and Exact Solutions in a Model of Hydrogen-Bonded-Chains"],"prefix":"10.1142","volume":"25","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":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fengjuan","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. S.","family":"Tchakoutio-Nguetcho","sequence":"additional","affiliation":[{"name":"Laboratoire Interdisciplinaire des Sciences et Sciences, Appliqu\u00e9es du Sahel (LISSAS), D\u00e9partement des Physiques, Universit\u00e9 de Maroua, BP 46, Maroua, Cameroon"},{"name":"Laboratoire LE2I UMR CNRS 6306, Aile des Sciences de l'ingnieur, Universit de Bourgogne, BP 47870, 21078 Dijon Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2015,5,3]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65138-0"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023639"},{"key":"rf3","volume-title":"Singular Nonlinear Traveling Wave Equations: Bifurcations and Exact Solutions","author":"Li J.","year":"2013"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414501600"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1140\/epjb\/e2007-00190-7"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127415500625","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:59:12Z","timestamp":1565117952000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127415500625"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4]]},"references-count":5,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2015,5,3]]},"published-print":{"date-parts":[[2015,4]]}},"alternative-id":["10.1142\/S0218127415500625"],"URL":"https:\/\/doi.org\/10.1142\/s0218127415500625","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4]]}}}