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By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions. <\/jats:p>","DOI":"10.1142\/s0218127416502072","type":"journal-article","created":{"date-parts":[[2016,11,22]],"date-time":"2016-11-22T02:46:26Z","timestamp":1479782786000},"page":"1650207","source":"Crossref","is-referenced-by-count":84,"title":["Understanding Peakons, Periodic Peakons and Compactons via a Shallow Water Wave Equation"],"prefix":"10.1142","volume":"26","author":[{"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. 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