{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T20:27:13Z","timestamp":1758400033147,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T00:00:00Z","timestamp":1667520000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T00:00:00Z","timestamp":1667520000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11801090"],"award-info":[{"award-number":["11801090"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"Postdoctoral Science Foundation of China","doi-asserted-by":"crossref","award":["2020M632593"],"award-info":[{"award-number":["2020M632593"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11901092"],"award-info":[{"award-number":["11901092"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2017A030310634"],"award-info":[{"award-number":["2017A030310634"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s00332-022-09866-x","type":"journal-article","created":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T16:03:44Z","timestamp":1667577824000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Non-uniform Continuity of the Generalized Camassa\u2013Holm Equation in Besov Spaces"],"prefix":"10.1007","volume":"33","author":[{"given":"Jinlu","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weipeng","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiayu","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,11,4]]},"reference":[{"key":"9866_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-16830-7","volume-title":"Fourier Analysis and Nonlinear Partial Differential Equations","author":"H Bahouri","year":"2011","unstructured":"Bahouri, H., Chemin, J., Danchin, R.: Fourier Analysis and Nonlinear Partial Differential Equations. Springer, Berlin (2011)"},{"key":"9866_CR2","doi-asserted-by":"publisher","first-page":"1661","DOI":"10.1103\/PhysRevLett.71.1661","volume":"71","author":"R Camassa","year":"1993","unstructured":"Camassa, R., Holm, D.: An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661\u20131664 (1993)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"9866_CR3","first-page":"53","volume":"15","author":"A Constantin","year":"1997","unstructured":"Constantin, A.: The Hamiltonian structure of the Camassa\u2013Holm equation. Expo. Math. 15(1), 53\u201385 (1997)","journal-title":"Expo. Math."},{"key":"9866_CR4","first-page":"303","volume":"26","author":"A Constantin","year":"1998","unstructured":"Constantin, A., Escher, J.: Global existence and blow-up for a shallow water equation. Ann. Scuola Norm. Sup. Pisa Classe Sci. 26, 303\u2013328 (1998)","journal-title":"Ann. Scuola Norm. Sup. Pisa Classe Sci."},{"key":"9866_CR5","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1002\/(SICI)1097-0312(199805)51:5<475::AID-CPA2>3.0.CO;2-5","volume":"51","author":"A Constantin","year":"1998","unstructured":"Constantin, A., Escher, J.: Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation. Commun. Pure Appl. Math. 51, 475\u2013504 (1998)","journal-title":"Commun. Pure Appl. Math."},{"key":"9866_CR6","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1098\/rspa.2000.0701","volume":"457","author":"A Constantin","year":"2001","unstructured":"Constantin, A.: On the scattering problem for the Camassa\u2013Holm equation. Proc. R. Soc. Lond. Ser. A 457, 953\u2013970 (2001)","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"9866_CR7","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1090\/S0273-0979-07-01159-7","volume":"44","author":"A Constantin","year":"2007","unstructured":"Constantin, A., Escher, J.: Particle trajectories in solitary water waves. Bull. Am. Math. Soc. 44, 423\u2013431 (2007)","journal-title":"Bull. Am. Math. Soc."},{"key":"9866_CR8","doi-asserted-by":"publisher","first-page":"559","DOI":"10.4007\/annals.2011.173.1.12","volume":"173","author":"A Constantin","year":"2011","unstructured":"Constantin, A., Escher, J.: Analyticity of periodic traveling free surface water waves with vorticity. Ann. Math. 173, 559\u2013568 (2011)","journal-title":"Ann. Math."},{"key":"9866_CR9","first-page":"953","volume":"14","author":"R Danchin","year":"2001","unstructured":"Danchin, R.: A few remarks on the Camassa\u2013Holm equation. Differ. Integral Equ. 14, 953\u2013988 (2001)","journal-title":"Differ. Integral Equ."},{"key":"9866_CR10","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1016\/S0022-0396(03)00096-2","volume":"192","author":"R Danchin","year":"2003","unstructured":"Danchin, R.: A note on well-posedness for Camassa\u2013Holm equation. J. Differ. Equ. 192, 429\u2013444 (2003)","journal-title":"J. Differ. Equ."},{"key":"9866_CR11","doi-asserted-by":"crossref","unstructured":"Fokas, A., Fuchssteiner, B.: Symplectic structures, their B\u00e4cklund transformation and hereditary symmetries, Phys. D, 4, 47-66 (1981\/1982)","DOI":"10.1016\/0167-2789(81)90004-X"},{"key":"9866_CR12","doi-asserted-by":"publisher","first-page":"1698","DOI":"10.1016\/j.jde.2018.08.013","volume":"266","author":"Z Guo","year":"2019","unstructured":"Guo, Z., Liu, X., Molinet, L., Yin, Z.: Ill-posedness of the Camassa-Holm and related equations in the critical space. J. Differ. Equ. 266, 1698\u20131707 (2019)","journal-title":"J. Differ. Equ."},{"key":"9866_CR13","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/j.jde.2022.04.020","volume":"327","author":"Y Guo","year":"2022","unstructured":"Guo, Y., Ye, W., Yin, Z.: Ill-posedness for the Cauchy problem of the Camassa\u2013Holm equation in $$B^1_{\\infty ,1}({\\mathbb{R} })$$. J. Differ. Equ. 327, 127\u2013144 (2022)","journal-title":"J. Differ. Equ."},{"key":"9866_CR14","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1081\/PDE-200059284","volume":"30","author":"S Hakkaev","year":"2005","unstructured":"Hakkaev, S., Kirchev, K.: Local well-posedness and orbital stability of solitary wave solutions for the generalized Camassa-Holm equation. Commun. Partial Differ. Equ. 30, 761\u2013781 (2005)","journal-title":"Commun. Partial Differ. Equ."},{"key":"9866_CR15","doi-asserted-by":"publisher","first-page":"3135","DOI":"10.1155\/IMRN.2005.3135","volume":"51","author":"A Himonas","year":"2005","unstructured":"Himonas, A., Misio\u0142ek, G.: High-frequency smooth solutions and well-posedness of the Camassa-Holm equation. Int. Math. Res. Not. 51, 3135\u20133151 (2005)","journal-title":"Int. Math. Res. Not."},{"key":"9866_CR16","first-page":"201","volume":"22","author":"A Himonas","year":"2009","unstructured":"Himonas, A., Kenig, C.: Non-uniform dependence on initial data for the CH equation on the line. Differ. Integr. Equ. 22, 201\u2013224 (2009)","journal-title":"Differ. Integr. Equ."},{"key":"9866_CR17","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1080\/03605300903436746","volume":"35","author":"A Himonas","year":"2010","unstructured":"Himonas, A., Kenig, C., Misio\u0142ek, G.: Non-uniform dependence for the periodic CH equation. Commun. Partial Differ. Equ. 35, 1145\u20131162 (2010)","journal-title":"Commun. Partial Differ. Equ."},{"key":"9866_CR18","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1215\/S0012-7094-01-10638-8","volume":"106","author":"C Kenig","year":"2001","unstructured":"Kenig, C., Ponce, G., Vega, L.: On the ill-posedness of some canonical dispersive equations. Duke Math. 106, 617\u2013633 (2001)","journal-title":"Duke Math."},{"key":"9866_CR19","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1007\/s00605-016-0927-8","volume":"183","author":"J Li","year":"2017","unstructured":"Li, J., Yin, Z.: Well-posedness and analytic solutions of the two-component Euler-Poincar\u00e9 system. Monatsh. Math. 183, 509\u2013537 (2017)","journal-title":"Monatsh. Math."},{"key":"9866_CR20","doi-asserted-by":"publisher","first-page":"6125","DOI":"10.1016\/j.jde.2016.08.031","volume":"261","author":"J Li","year":"2016","unstructured":"Li, J., Yin, Z.: Remarks on the well-posedness of Camassa-Holm type equations in Besov spaces. J. Differ. Equ. 261, 6125\u20136143 (2016)","journal-title":"J. Differ. Equ."},{"key":"9866_CR21","doi-asserted-by":"publisher","first-page":"8686","DOI":"10.1016\/j.jde.2020.06.028","volume":"269","author":"J Li","year":"2020","unstructured":"Li, J., Yu, Y., Zhu, W.: Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces. J. Differ. Equ. 269, 8686\u20138700 (2020)","journal-title":"J. Differ. Equ."},{"key":"9866_CR22","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1016\/j.jde.2021.10.052","volume":"306","author":"J Li","year":"2022","unstructured":"Li, J., Yu, Y., Zhu, W.: Ill-posedness for the Camassa-Holm and related equations in Besov spaces. J. Differ. Equ. 306, 403\u2013417 (2022)","journal-title":"J. Differ. Equ."},{"key":"9866_CR23","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.jmaa.2013.03.020","volume":"405","author":"Y Mi","year":"2013","unstructured":"Mi, Y., Mu, C.: Well-posedness and analyticity for the Cauchy problem for the generalized Camassa-Holm equation. J. Math. Anal. Appl. 405, 173\u2013182 (2013)","journal-title":"J. Math. Anal. Appl."},{"key":"9866_CR24","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1007\/s00605-014-0625-3","volume":"176","author":"Y Mi","year":"2015","unstructured":"Mi, Y., Mu, C.: On the Cauchy problem for the generalized Camassa-Holm equation. Monatsh. Math. 176, 423\u2013457 (2015)","journal-title":"Monatsh. Math."},{"key":"9866_CR25","doi-asserted-by":"publisher","first-page":"1358","DOI":"10.1080\/00036811.2013.833325","volume":"93","author":"W Yan","year":"2014","unstructured":"Yan, W., Li, Y., Zhang, Y.: The Cauchy problem for the generalized Camassa-Holm equation. Appl. Anal. 93, 1358\u20131381 (2014)","journal-title":"Appl. Anal."},{"key":"9866_CR26","doi-asserted-by":"publisher","first-page":"2876","DOI":"10.1016\/j.jde.2014.01.023","volume":"256","author":"W Yan","year":"2014","unstructured":"Yan, W., Li, Y., Zhang, Y.: The Cauchy problem for the generalized Camassa-Holm equation in Besov space. J. Differ. Equ. 256, 2876\u20132901 (2014)","journal-title":"J. Differ. Equ."}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-022-09866-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-022-09866-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-022-09866-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T11:13:59Z","timestamp":1673435639000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-022-09866-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,4]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["9866"],"URL":"https:\/\/doi.org\/10.1007\/s00332-022-09866-x","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"type":"print","value":"0938-8974"},{"type":"electronic","value":"1432-1467"}],"subject":[],"published":{"date-parts":[[2022,11,4]]},"assertion":[{"value":"24 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 November 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"6"}}