{"title":"Existence of periodic wave of a BBM equation with delay convection and weak diffusion","authors":"Minzhi Wei, Liping He","doi":"10.21203/rs.3.rs-2805124/v1","DOIUrl":null,"url":null,"abstract":"Abstract This paper focus on the existence and uniqueness of periodic waves for a BBM equation with local strong generic delay convection and weak diffusion. By analyzing the corresponding Hamiltonian system, we aim to obtain the existence of periodic orbit by constructing a locally invariant manifold according to geometric singular perturbation theory. Chebyshev criteria is applied to investigate the ratio of Abelian integrals. We prove the existence and uniqueness of periodic wave solution with sufficiently small perturbation parameter. Moreover, the upper and lower bounds of the limiting wave speed are given. Mathematics Subject Classification (2020) 34C25 · 34C60 · 37C27","PeriodicalId":500086,"journal":{"name":"Research Square (Research Square)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Research Square (Research Square)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21203/rs.3.rs-2805124/v1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This paper focus on the existence and uniqueness of periodic waves for a BBM equation with local strong generic delay convection and weak diffusion. By analyzing the corresponding Hamiltonian system, we aim to obtain the existence of periodic orbit by constructing a locally invariant manifold according to geometric singular perturbation theory. Chebyshev criteria is applied to investigate the ratio of Abelian integrals. We prove the existence and uniqueness of periodic wave solution with sufficiently small perturbation parameter. Moreover, the upper and lower bounds of the limiting wave speed are given. Mathematics Subject Classification (2020) 34C25 · 34C60 · 37C27
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
