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Higher Dimensional Camassa–Holm Equations |
| S. Y. Lou1, Man Jia1*, and Xia-Zhi Hao2* |
1School of Physical Science and Technology, Ningbo University, Ningbo 315211, China
2Faculty of Science, Zhejiang University of Technology, Hangzhou 310014, China
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| Cite this article: |
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S. Y. Lou, Man Jia, and Xia-Zhi Hao 2023 Chin. Phys. Lett. 40 020201 |
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Abstract Utilizing some conservation laws of the (1+1)-dimensional Camassa–Holm (CH) equation and/or its reciprocal forms, some (n+1)-dimensional CH equations for $n\geq 1$ are constructed by a modified deformation algorithm. The Lax integrability can be proven by applying the same deformation algorithm to the Lax pair of the (1+1)-dimensional CH equation. A novel type of peakon solution is implicitly given and expressed by the LambertW function.
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Received: 01 January 2023
Editors' Suggestion
Published: 06 February 2023
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| PACS: |
02.30.Ik
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(Integrable systems)
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05.45.Yv
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(Solitons)
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47.20.Ky
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(Nonlinearity, bifurcation, and symmetry breaking)
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52.35.Mw
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(Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))
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52.35.Sb\\
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| [1] | Lou S Y and Ni G J 1989 Phys. Lett. A 140 33 |
| [2] | Hu H C, Lou S Y, and Chow K W 2007 Chaos Solitons & Fractals 31 1213 |
| [3] | Lou S Y 1997 J. Phys. A 30 7259 |
| [4] | Lou S Y, Hao X Z, and Jia M 2022 arXiv:2211.06844 [nlin.SI] |
| [5] | Ablowitz M J and Musslimani Z H 2013 Phys. Rev. Lett. 110 064105 |
| [6] | Lou S Y 2018 J. Math. Phys. 59 083507 |
| [7] | Camassa R and Holm D D 1993 Phys. Rev. Lett. 71 1661 |
| [8] | Fuchssteiner B and Fokas A 1981 Physica D 4 47 |
| [9] | Constantin A and Strauss W 2000 Phys. Lett. A 270 140 |
| [10] | Dai H H 1998 Acta Mech. 127 193 |
| [11] | Hunter J K and Saxton R 1991 SIAM J. Appl. Math. 51 1498 |
| [12] | Bressan A and Constantin A 2005 SIAM J. Math. Anal. 37 996 |
| [13] | Loewner C 1952 J. Anal. Math. 2 219 |
| [14] | Konopelchenko B and Rogers C 1991 Phys. Lett. A 158 391 |
| [15] | Lou S Y, Rogers C, and Schief W K 2003 J. Math. Phys. 44 5869 |
| [16] | Oevel W and Schief W K 1994 Rev. Math. Phys. 6 1301 |
| [17] | Lou S Y 2003 J. Phys. A 36 3877 |
| [18] | Konopelchenko B G and Rogers C 1993 J. Math. Phys. 34 214 |
| [19] | Schief W K 1994 Proc. R. Soc. A|Proc. R. Soc. London Ser. A 446 381 |
| [20] | Lou S Y and Qiao Z J 2017 Chin. Phys. Lett. 34 100201 |
| [21] | Zhang D J and Chen D Y 2002 Chaos Solitons & Fractals 14 573 |
| [22] | Wang D S, Li Q, Wen X Y, and Liu L 2020 Rep. Math. Phys. 86 325 |
| [23] | Lü X and Ma W X 2016 Nonlinear Dyn. 85 1217 |
| [24] | Wang D S, Guo B L, and Wang X L 2019 J. Differ. Equ. 266 5209 |
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