{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T17:25:00Z","timestamp":1775755500440,"version":"3.50.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p> This paper studies two two-component shallow water wave models. From the dynamical systems approach and using the singular traveling wave theory developed by Li and Chen [2007], all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are obtained under different parameter conditions. More than six explicit exact parametric representations are derived. More interestingly, it was found that, for the two-component Camassa\u2013Holm equations with constant vorticity, its [Formula: see text]-traveling wave system has a pseudo-peakon wave solution. In addition, its [Formula: see text]-traveling wave system has four families of uncountably infinitely many solitary wave solutions. The new results complete a recent study of Dutykh and Ionescu-Kruse [2019]. <\/jats:p>","DOI":"10.1142\/s0218127421500012","type":"journal-article","created":{"date-parts":[[2021,1,26]],"date-time":"2021-01-26T08:44:35Z","timestamp":1611650675000},"page":"2150001","source":"Crossref","is-referenced-by-count":12,"title":["Bifurcations and Exact Traveling Wave Solutions of Two Shallow Water Two-Component Systems"],"prefix":"10.1142","volume":"31","author":[{"given":"Jibin","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"},{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejing 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanrong","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,1,25]]},"reference":[{"key":"S0218127421500012BIB001","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-65138-0","volume-title":"Handbook of Elliptic Integrals for Engineers and Scientists","author":"Byrd P. 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