On peaked and smooth solitons for the Camassa-Holm equationZ. J. Qiao1 and G. P. Zhang2
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
received 23 October 2005; accepted in final form 6 January 2006
published online 25 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 A=0. 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.
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