{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:01:25Z","timestamp":1760230885563,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,16]],"date-time":"2022-08-16T00:00:00Z","timestamp":1660608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangxi Key Laboratory of Cryptography and Information Security","award":["GCIS202134","YCSW2022291"],"award-info":[{"award-number":["GCIS202134","YCSW2022291"]}]},{"name":"Innovation Project of Guangxi Graduate Education","award":["GCIS202134","YCSW2022291"],"award-info":[{"award-number":["GCIS202134","YCSW2022291"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Peakons and periodic peakons are two kinds of special symmetric traveling wave solutions, which have important applications in physics, optical fiber communication, and other fields. In this paper, we study the orbital stability of peakons and periodic peakons for a generalized Camassa\u2013Holm equation with quadratic and cubic nonlinearities (mCH\u2013Novikov\u2013CH equation). It is a generalization of some classical equations, such as the Camassa\u2013Holm (CH) equation, the modified Camassa\u2013Holm (mCH) equation, and the Novikov equation. By constructing an inequality related to the maximum and minimum of solutions with the conservation laws, we prove that the peakons and periodic peakons are orbitally stable under small perturbations in the energy space.<\/jats:p>","DOI":"10.3390\/sym14081702","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T03:15:27Z","timestamp":1660706127000},"page":"1702","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stability of Peakons and Periodic Peakons for the mCH\u2013Novikov\u2013CH Equation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9239-1410","authenticated-orcid":false,"given":"Kelei","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianguo","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengqiang","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,16]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"The cauchy problem and multi-peakons for the mCH\u2013Novikov\u2013CH equation with quadratic and cubic nonlinearities","volume":"2022","author":"Qin","year":"2022","journal-title":"J. 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