{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T07:37:56Z","timestamp":1773387476243,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p> In this paper, we consider variform exact peakon solutions for four nonlinear wave equations. We show that under different parameter conditions, one nonlinear wave equation can have different exact one-peakon solutions and different nonlinear wave equations can have different explicit exact one-peakon solutions. Namely, there are various explicit exact one-peakon solutions, which are different from the one-peakon solution pe<jats:sup>-\u03b1|x-ct|<\/jats:sup>. In fact, when a traveling system has a singular straight line and a curve triangle surrounding a periodic annulus of a center under some parameter conditions, there exists peaked solitary wave solution (peakon). <\/jats:p>","DOI":"10.1142\/s0218127414501600","type":"journal-article","created":{"date-parts":[[2015,1,5]],"date-time":"2015-01-05T06:43:47Z","timestamp":1420440227000},"page":"1450160","source":"Crossref","is-referenced-by-count":13,"title":["Variform Exact One-Peakon Solutions for Some Singular Nonlinear Traveling Wave Equations of the First Kind"],"prefix":"10.1142","volume":"24","author":[{"given":"Jibin","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"},{"name":"Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2015,1,4]]},"reference":[{"key":"rf1","first-page":"L1CL4","volume":"15","author":"Beals B.","year":"1999","journal-title":"Inver. Probl."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.71.1661"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-2156(08)70254-0"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-005-0041-7"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2011.556695"},{"key":"rf6","doi-asserted-by":"crossref","unstructured":"A.\u00a0Degasperis and A. M.\u00a0Procesi, Symmetry and Perturbation Theory, eds. 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