{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T16:03:52Z","timestamp":1760889832389,"version":"3.37.3"},"reference-count":15,"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":["11571318","11162020"],"award-info":[{"award-number":["11571318","11162020"]}],"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":[[2019,4]]},"abstract":"<jats:p> For a singular nonlinear traveling wave system of the first class, if there exist two node points of the associated regular system in the singular straight line, then the dynamics of the solutions of the singular system will be very complex. In this paper, two representative nonlinear traveling wave system models (namely, the traveling wave system of Green\u2013Naghdi equations and the traveling wave system of the Raman soliton model for optical metamaterials) are investigated. It is shown that, if there exist two node points of the associated regular system in the singular straight line, then the singular system has no peakon, periodic peakon and compacton solutions, but rather, it has smooth periodic wave, solitary wave and kink wave solutions. <\/jats:p>","DOI":"10.1142\/s0218127419500470","type":"journal-article","created":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T06:22:39Z","timestamp":1555914159000},"page":"1950047","source":"Crossref","is-referenced-by-count":4,"title":["Smooth Exact Traveling Wave Solutions Determined by Singular Nonlinear Traveling Wave Systems: Two Models"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4839-5956","authenticated-orcid":false,"given":"Jibin","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"},{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanrong","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengfu","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. 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