{"title":"Orbital stability of the trains of peaked solitary waves for the modified Camassa-Holm-Novikov equation","authors":"Ting Luo","doi":"10.1515/anona-2023-0124","DOIUrl":null,"url":null,"abstract":"\n Consideration herein is the stability issue of peaked solitary wave solution for the modified Camassa-Holm-Novikov equation, which is derived from the shallow water theory. This wave configuration accommodates the ordered trains of the modified Camassa-Holm-Novikov-peaked solitary solution. With the application of conservation laws and the monotonicity property of the localized energy functionals, we prove the orbital stability of this wave profile in the \n \n \n \n \n \n H\n \n \n 1\n \n \n \n (\n \n R\n \n )\n \n \n {H}^{1}\\left({\\mathbb{R}})\n \n energy space according to the modulation argument.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":3.2000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/anona-2023-0124","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Consideration herein is the stability issue of peaked solitary wave solution for the modified Camassa-Holm-Novikov equation, which is derived from the shallow water theory. This wave configuration accommodates the ordered trains of the modified Camassa-Holm-Novikov-peaked solitary solution. With the application of conservation laws and the monotonicity property of the localized energy functionals, we prove the orbital stability of this wave profile in the
H
1
(
R
)
{H}^{1}\left({\mathbb{R}})
energy space according to the modulation argument.
本文考虑的是修正的卡马萨-霍尔姆-诺维科夫方程的峰状孤波解的稳定性问题，该方程源于浅水理论。这种波形构造可容纳修正的卡马萨-霍尔姆-诺维科夫峰孤波解的有序波列。通过应用守恒定律和局部能量函数的单调性，我们根据调制论证证明了该波谱在 H 1 ( R ) {H}^{1}\left({mathbb{R}}) 能量空间中的轨道稳定性。
期刊介绍：
Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.
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