{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:43:48Z","timestamp":1740120228220,"version":"3.37.3"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["(11471289,11571318)"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,4]]},"abstract":" In this paper, we show that to find the traveling wave solutions for the Krichever\u2013Novikov equation, we only need to consider a spatial form F-VI of the fourth-order differential equations in the polynomial class having the Painlev\u00e9 property given by [Cosgrove, 2000]. By using the method of dynamical systems to analyze the dynamical behavior of the traveling wave solutions in some two-dimensional invariant manifolds, various exact solutions such as solitary wave solution, periodic wave solutions, quasi-periodic wave solutions and uncountably infinitely many unbounded wave solutions are obtained. <\/jats:p>","DOI":"10.1142\/s0218127417500584","type":"journal-article","created":{"date-parts":[[2017,5,8]],"date-time":"2017-05-08T05:30:57Z","timestamp":1494221457000},"page":"1750058","source":"Crossref","is-referenced-by-count":1,"title":["Exact Traveling Wave Solutions of the Krichever\u2013Novikov Equation: A Dynamical System Approach"],"prefix":"10.1142","volume":"27","author":[{"given":"KitIan","family":"Kou","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Macau, Macau, P. R. China"}]},{"given":"Jibin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2017,5,8]]},"reference":[{"key":"S0218127417500584BIB001","doi-asserted-by":"publisher","DOI":"10.1155\/S1073792898000014"},{"key":"S0218127417500584BIB002","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/49\/10\/105201"},{"key":"S0218127417500584BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s11232-011-0071-5"},{"key":"S0218127417500584BIB004","doi-asserted-by":"publisher","DOI":"10.1002\/mma.1578"},{"key":"S0218127417500584BIB005","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9590.00130"},{"key":"S0218127417500584BIB006","doi-asserted-by":"publisher","DOI":"10.1142\/S1402925109000340"},{"key":"S0218127417500584BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2013.06.011"},{"key":"S0218127417500584BIB008","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/35\/46\/306"},{"key":"S0218127417500584BIB009","first-page":"650","volume":"20","author":"Krichever I. M.","year":"1979","journal-title":"Sov. Math. Dokl."},{"key":"S0218127417500584BIB010","doi-asserted-by":"publisher","DOI":"10.1070\/RM1980v035n06ABEH001974"},{"key":"S0218127417500584BIB011","first-page":"097","volume":"7","author":"Levi D.","year":"2011","journal-title":"Symm. Integrab. Geom.: Meth. Appl."},{"key":"S0218127417500584BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(02)00287-6"},{"key":"S0218127417500584BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/BF02557203"},{"key":"S0218127417500584BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/BF01077866"},{"key":"S0218127417500584BIB015","first-page":"165","volume":"28","author":"Svinolupov S. I.","year":"1983","journal-title":"Sov. Math. Dokl."},{"key":"S0218127417500584BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2012.02.053"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417500584","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:36:55Z","timestamp":1565138215000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417500584"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4]]},"references-count":16,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2017,5,8]]},"published-print":{"date-parts":[[2017,4]]}},"alternative-id":["10.1142\/S0218127417500584"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417500584","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2017,4]]}}}