{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:22:12Z","timestamp":1760235732110,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T00:00:00Z","timestamp":1632268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we study the symmetric travelling wave solutions of the b-family of the Novikov equation. We show that the b-family of the Novikov equation can provide symmetric travelling wave solutions, such as peakon, kink and smooth soliton solutions. In particular, the single peakon, two-peakon, stationary kink, anti-kink, two-kink, two-anti-kink, bell-shape soliton and hat-shape soliton solutions are presented in an explicit formula.<\/jats:p>","DOI":"10.3390\/sym13101765","type":"journal-article","created":{"date-parts":[[2021,9,22]],"date-time":"2021-09-22T22:50:48Z","timestamp":1632351048000},"page":"1765","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Solutions of the b-Family of Novikov Equation"],"prefix":"10.3390","volume":"13","author":[{"given":"Tingting","family":"Wang","sequence":"first","affiliation":[{"name":"Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China"}]},{"given":"Xuanxuan","family":"Han","sequence":"additional","affiliation":[{"name":"Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China"}]},{"given":"Yibin","family":"Lu","sequence":"additional","affiliation":[{"name":"Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/S0375-9601(03)00114-2","article-title":"Nonlinear balance and exchange of stability of dynamics of solitons, peakons, ramps\/cliffs and leftons in a 1 + 1 nonlinear evolutionary PDE","volume":"308","author":"Holm","year":"2003","journal-title":"Phys. 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