%0 Journal Article
%T Periodic blow-up solutions and their limit forms for the generalized Camassa–Holm equation
%A Zhengrong Liu
%A Boling Guo
%J 自然科学进展
%D 2008
%I 
%X In this paper, we consider the generalized Camassa–Holm equation ut + 2kux - uxxt + au2ux=2uxuxx + uuxxx. Under substitution ξ x = ct, some new explicit periodic wave solutions and their limit forms are presented through some special phase orbits. These periodic wave solutions tend to in?nity on ξ- u plane periodically. Thus we call them periodic blow-up solutions. To our knowledge, such periodic blow-up solutions have not been found in any other equations.
%K Generalized
%K Camassa–Holm
%K equation
%K Explicit
%K solutions
%K Periodic
%K blow-up
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=01BA20E8BA813E1908F3698710BBFEFEE816345F465FEBA5&cid=96E6E851B5104576C2DD9FC1FBCB69EF&jid=504AF8C1E5476CA7C4EC9DF6FEAC14AC&aid=00DEBF27E8243C9FBA44885730D72D55&yid=67289AFF6305E306&vid=13553B2D12F347E8&iid=38B194292C032A66&sid=0F7768518993EDDE&eid=4FE459D71E3BF8EB&journal_id=1002-008X&journal_name=自然科学进展&referenced_num=0&reference_num=0