New periodic exact traveling wave solutions of Camassa–Holm equation
In Zhang et al. (2007) and Zhang (2021) we constructed all single-peak traveling wave solutions of the Camassa–Holm equation including some explicit solutions. In general it is a challenge to construct exact multi-peak traveling wave solutions. As an example a periodic traveling wave (or wavetrain),...
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| Published in | Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters Vol. 6; p. 100426 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.12.2022
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2666-8181 2666-8181 |
| DOI | 10.1016/j.padiff.2022.100426 |
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| Abstract | In Zhang et al. (2007) and Zhang (2021) we constructed all single-peak traveling wave solutions of the Camassa–Holm equation including some explicit solutions. In general it is a challenge to construct exact multi-peak traveling wave solutions. As an example a periodic traveling wave (or wavetrain), a special type of spatiotemporal oscillation that is a periodic function of both space and time, plays a fundamental role in many mathematical equations such as shallow water wave equations. In this paper we will construct some new exact periodic traveling wave solutions of the Camassa–Holm equation. |
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| AbstractList | In Zhang et al. (2007) and Zhang (2021) we constructed all single-peak traveling wave solutions of the Camassa–Holm equation including some explicit solutions. In general it is a challenge to construct exact multi-peak traveling wave solutions. As an example a periodic traveling wave (or wavetrain), a special type of spatiotemporal oscillation that is a periodic function of both space and time, plays a fundamental role in many mathematical equations such as shallow water wave equations. In this paper we will construct some new exact periodic traveling wave solutions of the Camassa–Holm equation. |
| ArticleNumber | 100426 |
| Author | Zhang, Guoping |
| Author_xml | – sequence: 1 givenname: Guoping surname: Zhang fullname: Zhang, Guoping email: guoping.zhang@morgan.edu organization: Department of Mathematics, Morgan State University, 1700 E Cold Spring Ln, Baltimore, MD 21239, USA |
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| Cites_doi | 10.1098/rspa.2000.0520 10.1103/PhysRevLett.71.1661 10.1002/(SICI)1097-0312(199908)52:8<949::AID-CPA3>3.0.CO;2-D 10.1007/BF02392586 10.4171/RMI/339 10.1023/B:JODY.0000041284.26400.d0 10.1016/0167-2789(81)90004-X 10.1016/j.jde.2004.09.007 10.1007/s00332-002-0517-x 10.1007/s11040-007-9027-2 10.1006/jfan.1997.3231 |
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| Keywords | 34A05 34B15 34A34 Camassa–Holm equation 34B40 Cuspon solution Periodic Explicit solution 35C08 Traveling wave solution 35A09 35C07 |
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