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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/9363673 |
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| _version_ | 1832560969391276032 |
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| author | Hao Yu Aiyong Chen Kelei Zhang |
| author_facet | Hao Yu Aiyong Chen Kelei Zhang |
| author_sort | Hao Yu |
| collection | DOAJ |
| 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 |
| id | doaj-art-c7e561631d2342d5b4da5e9590ac803c |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-c7e561631d2342d5b4da5e9590ac803c2025-02-03T01:26:24ZengWileyAdvances in Mathematical Physics1687-91392021-01-01202110.1155/2021/9363673Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH EquationHao Yu0Aiyong Chen1Kelei Zhang2School of Mathematics and Computing ScienceSchool of Mathematics and Computing ScienceSchool of Mathematics and Computing ScienceFor 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.http://dx.doi.org/10.1155/2021/9363673 |
| spellingShingle | Hao Yu Aiyong Chen Kelei Zhang Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation Advances in Mathematical Physics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2021/9363673 |
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