On the blow-up of solutions to the integrable modified Camassa-Holm equation

Yue Liu; Peter J. Olver; Changzheng Qu; Shuanghu Zhang

doi:10.1142/S0219530514500274

On the blow-up of solutions to the integrable modified Camassa-Holm equation

Yue Liu, Peter J. Olver, Changzheng Qu, Shuanghu Zhang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

Abstract

We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the modified integrable Camassa-Holm equation with cubic nonlinearity. The blow-up conditions are formulated in terms of the initial momentum density and the average initial energy.

Original language	English (US)
Pages (from-to)	355-368
Number of pages	14
Journal	Analysis and Applications
Volume	12
Issue number	4
DOIs	https://doi.org/10.1142/S0219530514500274
State	Published - Jul 2014

Bibliographical note

Funding Information:
The work of Liu is partially supported by the NSF grant DMS-1207840 and the NSF-China grant 11271192. The work of Olver is partially supported by NSF grant DMS-1108894. The work of Qu is supported in part by the NSF-China for Distinguished Young Scholars grant 10925104. The work of Zhang is partially supported by the NSF of China under the grant 11101337, Doctoral Foundation of Ministry of Education of China grant 20110182120013, Fundamental Research Funds for the Central Universities grant XDJK2011C046, and China Scholarship Council.

Keywords

Blow up
Integrable equation
Modified Camassa-Holm equation
Peakon

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10.1142/S0219530514500274

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abstract = "We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the modified integrable Camassa-Holm equation with cubic nonlinearity. The blow-up conditions are formulated in terms of the initial momentum density and the average initial energy.",

keywords = "Blow up, Integrable equation, Modified Camassa-Holm equation, Peakon",

author = "Yue Liu and Olver, {Peter J.} and Changzheng Qu and Shuanghu Zhang",

note = "Funding Information: The work of Liu is partially supported by the NSF grant DMS-1207840 and the NSF-China grant 11271192. The work of Olver is partially supported by NSF grant DMS-1108894. The work of Qu is supported in part by the NSF-China for Distinguished Young Scholars grant 10925104. The work of Zhang is partially supported by the NSF of China under the grant 11101337, Doctoral Foundation of Ministry of Education of China grant 20110182120013, Fundamental Research Funds for the Central Universities grant XDJK2011C046, and China Scholarship Council.",

year = "2014",

month = jul,

doi = "10.1142/S0219530514500274",

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T1 - On the blow-up of solutions to the integrable modified Camassa-Holm equation

AU - Liu, Yue

AU - Olver, Peter J.

AU - Qu, Changzheng

AU - Zhang, Shuanghu

N1 - Funding Information: The work of Liu is partially supported by the NSF grant DMS-1207840 and the NSF-China grant 11271192. The work of Olver is partially supported by NSF grant DMS-1108894. The work of Qu is supported in part by the NSF-China for Distinguished Young Scholars grant 10925104. The work of Zhang is partially supported by the NSF of China under the grant 11101337, Doctoral Foundation of Ministry of Education of China grant 20110182120013, Fundamental Research Funds for the Central Universities grant XDJK2011C046, and China Scholarship Council.

PY - 2014/7

Y1 - 2014/7

N2 - We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the modified integrable Camassa-Holm equation with cubic nonlinearity. The blow-up conditions are formulated in terms of the initial momentum density and the average initial energy.

AB - We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the modified integrable Camassa-Holm equation with cubic nonlinearity. The blow-up conditions are formulated in terms of the initial momentum density and the average initial energy.

KW - Blow up

KW - Integrable equation

KW - Modified Camassa-Holm equation

KW - Peakon

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On the blow-up of solutions to the integrable modified Camassa-Holm equation

Abstract

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Keywords

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