Article ID Journal Published Year Pages File Type
1868106 Physics Letters A 2006 7 Pages PDF
Abstract

A simple method is developed for constructing the solutions of the short-wave model equations associated with the Camassa–Holm (CH) and Degasperis–Procesi (DP) shallow-water wave equations. Taking an appropriate scaling limit of the N-soliton solution of the CH equation, we obtain the N-cusp soliton solution for the CH short-wave model. The similar procedure also leads to the N-loop soliton solution for the DP short-wave model. We describe the property of the solutions. In particular, we derive the large-time asymptotics of the solutions as well as the formulas for the phase shift.

Related Topics
Physical Sciences and Engineering Physics and Astronomy Physics and Astronomy (General)
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