Z. J. Qiao and G. P. Zhang 2006 Europhys. Lett. 73 657 doi:10.1209/epl/i2005-10453-y
Z. J. Qiao1 and G. P. Zhang2
Show affiliationsThis letter presents all possible explicit single soliton solutions for the Camassa-Holm (CH) equation mt + mxu + 2mux = 0, m = u − uxx. This equation is studied under the boundary condition u → A (A is a constant) as x → ±∞. Regular peakon solutions correspond to the case of A = 0. For the case of A ≠ 0, 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.
Issue 5 (March 2006)
Received 23 October 2005, accepted for publication 6 January 2006, in final form 6 January 2006
Published 25 January 2006
Z. J. Qiao and G. P. Zhang 2006 Europhys. Lett. 73 657
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