Deltons, peakons and other traveling-wave solutions of a Camassa-Holm hierarchy
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Pages (from-to) | 2454-2460 |
Journal / Publication | Physics Letters, Section A: General, Atomic and Solid State Physics |
Volume | 373 |
Issue number | 29 |
Publication status | Published - 29 Jun 2009 |
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Abstract
In this letter, we study an integrable Camassa-Holm hierarchy whose high-frequency limit is the Camassa-Holm equation. Phase plane analysis is employed to investigate bounded traveling wave solutions. An important feature is that there exists a singular line on the phase plane. By considering the properties of the equilibrium points and the relative position of the singular line, we find that there are in total three types of phase planes. Those paths in phase planes which represented bounded solutions are discussed one-by-one. Besides solitary, peaked and periodic waves, the equations are shown to admit a new type of traveling waves, which concentrate all their energy in one point, and we name them deltons as they can be expressed as some constant multiplied by a delta function. There also exists a type of traveling waves we name periodic deltons, which concentrate their energy in periodic points. The explicit expressions for them and all the other traveling waves are given. © 2009 Elsevier B.V. All rights reserved.
Research Area(s)
- Camassa-Holm hierarchy, Deltons, Peakons, Solitons
Citation Format(s)
Deltons, peakons and other traveling-wave solutions of a Camassa-Holm hierarchy. / Peng, Xiaochun; Dai, Hui-Hui.
In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 373, No. 29, 29.06.2009, p. 2454-2460.
In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 373, No. 29, 29.06.2009, p. 2454-2460.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review