{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T11:42:16Z","timestamp":1751542936360,"version":"3.37.3"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471289"],"award-info":[{"award-number":["11471289"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11162020"],"award-info":[{"award-number":["11162020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p> In this paper, we consider the traveling wave solutions for a shallow water equation. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. On the basis of the theory of the singular traveling wave systems, we obtain the bifurcations of phase portraits and explicit exact parametric representations for solitary wave solutions and smooth periodic wave solutions, as well as periodic peakon solutions. We show the existence of compacton solutions of the equation under different parameter conditions. <\/jats:p>","DOI":"10.1142\/s0218127416501728","type":"journal-article","created":{"date-parts":[[2016,9,23]],"date-time":"2016-09-23T05:53:59Z","timestamp":1474610039000},"page":"1650172","source":"Crossref","is-referenced-by-count":1,"title":["Exact Traveling Wave Solutions and Bifurcations for a Shallow Water Equation Modeling Surface Waves of Moderate Amplitude"],"prefix":"10.1142","volume":"26","author":[{"given":"Wenjing","family":"Zhu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jibin","family":"Li","sequence":"additional","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"}]}],"member":"219","published-online":{"date-parts":[[2016,9,23]]},"reference":[{"key":"S0218127416501728BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65138-0"},{"key":"S0218127416501728BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-008-0128-2"},{"key":"S0218127416501728BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2014.02.005"},{"key":"S0218127416501728BIB004","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112001007224"},{"key":"S0218127416501728BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.11.038"},{"key":"S0218127416501728BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.09.007"},{"key":"S0218127416501728BIB007","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2007.2009"},{"key":"S0218127416501728BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407019858"},{"key":"S0218127416501728BIB009","first-page":"1250305-1","volume":"22","author":"Li J.","year":"2012","journal-title":"Int. J. Bifurcation and Chaos"},{"volume-title":"Singular Nonlinear Traveling Wave Equations: Bifurcations and Exact Solutions","year":"2013","author":"Li J.","key":"S0218127416501728BIB010"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416501728","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,25]],"date-time":"2019-09-25T02:19:04Z","timestamp":1569377944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416501728"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9]]},"references-count":10,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2016,9,23]]},"published-print":{"date-parts":[[2016,9]]}},"alternative-id":["10.1142\/S0218127416501728"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416501728","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2016,9]]}}}