| Issue |
Europhys. Lett.
Volume 73, Number 5, March 2006
|
|
|---|---|---|
| Page(s) | 657 - 663 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2005-10453-y | |
| Published online | 25 January 2006 | |
On peaked and smooth solitons for the Camassa-Holm equation
1
Department of Mathematics, The University of Texas-Pan American 1201 W University Drive, Edinburg, TX 78541, USA
2
Applied Mathematics Research Center, Delaware State University 1200 North Dupont Highway, Dover, DE 19901, USA
Corresponding author: qiao@utpa.edu
Received:
23
October
2005
Accepted:
6
January
2006
This letter presents all possible explicit single soliton solutions
for the Camassa-Holm (CH) equation 
. This equation is studied under the boundary condition 
(A is a constant) as 
.
Regular peakon solutions correspond to the case of 
. For the
case of 
, both new peaked solitons and new type of smooth
solitons, which are expressed in terms of trigonometric and
hyperbolic functions, are tremendously given through investigating
a Newton equation with a new potential. Mathematical analysis and
numeric graphs are provided for those smooth soliton and new peaked
soliton solutions.
PACS: 02.30.Ik – Integrable systems / 05.45.Yv – Solitons / 03.75.Lm – Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations
© EDP Sciences, 2006
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