Volume 73, Number 5, March 2006
|Page(s)||657 - 663|
|Published online||25 January 2006|
On peaked and smooth solitons for the Camassa-Holm equation
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: firstname.lastname@example.org
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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