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Article: Stability of peakons of the Camassa–Holm equation beyond wave breaking
| Title | Stability of peakons of the Camassa–Holm equation beyond wave breaking |
|---|---|
| Authors | |
| Issue Date | 1-Dec-2022 |
| Publisher | American Institute of Physics |
| Citation | Journal of Mathematical Physics, 2022, v. 63, n. 12 How to Cite? |
| Abstract | Using a generalized framework that consists of evolution of the solution to the Camassa–Holm equation and its energy measure, we establish the global-in-time orbital stability of peakons with respect to the perturbed (energy) conservative solutions to the Camassa–Holm equation. In particular, we extend the H1-stability result obtained by Constantin and Strauss [Commun. Pure Appl. Math. 53(5), 603–610 (2000)] globally-in-time even after the perturbed solutions experience wave breaking. In addition, our result also shows that the singular part of the energy measure of the perturbed solutions will remain stable for all times. |
| Persistent Identifier | http://hdl.handle.net/10722/331358 |
| ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 0.569 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Gao, Yu | - |
| dc.contributor.author | Liu, Hao | - |
| dc.contributor.author | Wong, Tak, Kwong | - |
| dc.date.accessioned | 2023-09-21T06:55:02Z | - |
| dc.date.available | 2023-09-21T06:55:02Z | - |
| dc.date.issued | 2022-12-01 | - |
| dc.identifier.citation | Journal of Mathematical Physics, 2022, v. 63, n. 12 | - |
| dc.identifier.issn | 0022-2488 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/331358 | - |
| dc.description.abstract | <p>Using a generalized framework that consists of evolution of the solution to the Camassa–Holm equation and its energy measure, we establish the global-in-time orbital stability of peakons with respect to the perturbed (energy) conservative solutions to the Camassa–Holm equation. In particular, we extend the <em>H</em><sup>1</sup>-stability result obtained by Constantin and Strauss [Commun. Pure Appl. Math. <strong>53</strong>(5), 603–610 (2000)] globally-in-time even after the perturbed solutions experience wave breaking. In addition, our result also shows that the singular part of the energy measure of the perturbed solutions will remain stable for all times.<br></p> | - |
| dc.language | eng | - |
| dc.publisher | American Institute of Physics | - |
| dc.relation.ispartof | Journal of Mathematical Physics | - |
| dc.title | Stability of peakons of the Camassa–Holm equation beyond wave breaking | - |
| dc.type | Article | - |
| dc.identifier.doi | 10.1063/5.0110552 | - |
| dc.identifier.scopus | eid_2-s2.0-85144360701 | - |
| dc.identifier.volume | 63 | - |
| dc.identifier.issue | 12 | - |
| dc.identifier.eissn | 1089-7658 | - |
| dc.identifier.isi | WOS:000893036200016 | - |
| dc.identifier.issnl | 0022-2488 | - |