Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation

For the generalized mCH equation, we construct a 2-peakon solution on both the line and the circle, and we can control the size of the initial data. The two peaks at different speeds move in the same direction and eventually collide. This phenomenon is that the solution at the collision time is cons...

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Autores principales:	Hao Yu, Aiyong Chen, Kelei Zhang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/c7e561631d2342d5b4da5e9590ac803c
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spelling	oai:doaj.org-article:c7e561631d2342d5b4da5e9590ac803c2021-11-22T01:10:01ZConstruction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation1687-913910.1155/2021/9363673https://doaj.org/article/c7e561631d2342d5b4da5e9590ac803c2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/9363673https://doaj.org/toc/1687-9139For the generalized mCH equation, we construct a 2-peakon solution on both the line and the circle, and we can control the size of the initial data. The two peaks at different speeds move in the same direction and eventually collide. This phenomenon is that the solution at the collision time is consistent with another solitary peakon solution. By reversing the time, we get two new solutions with the same initial value and different values at the rest of the time, which means the nonuniqueness for the equation in Sobolev spaces Hs is proved for s<3/2.Hao YuAiyong ChenKelei ZhangHindawi LimitedarticlePhysicsQC1-999ENAdvances in Mathematical Physics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Hao Yu Aiyong Chen Kelei Zhang Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation
description	For the generalized mCH equation, we construct a 2-peakon solution on both the line and the circle, and we can control the size of the initial data. The two peaks at different speeds move in the same direction and eventually collide. This phenomenon is that the solution at the collision time is consistent with another solitary peakon solution. By reversing the time, we get two new solutions with the same initial value and different values at the rest of the time, which means the nonuniqueness for the equation in Sobolev spaces Hs is proved for s<3/2.
format	article
author	Hao Yu Aiyong Chen Kelei Zhang
author_facet	Hao Yu Aiyong Chen Kelei Zhang
author_sort	Hao Yu
title	Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation
title_short	Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation
title_full	Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation
title_fullStr	Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation
title_full_unstemmed	Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation
title_sort	construction of 2-peakon solutions and nonuniqueness for a generalized mch equation
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/c7e561631d2342d5b4da5e9590ac803c
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Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation

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