Abstract:The Camassa–Holm equationu_{t}−u_{xxt}+3uu_{x}−2u_{x}u_{xx}−uu_{xxx}=0 enjoys special solutions of the formu(x,t)=∑_{i}p_{i}(t)exp(-|x-q_{i}(t|), denoted multipeakons, that interact in a way similar to that of solitons. We show that given initial datau|_{t=0}=u_{0}inH^{1}(R) such thatu−u_{xx}is a positive Radon measure, one can construct a sequence of multipeakons that converges inL^{∞}_{loc}(R,H^{1}_{loc}(R)) to the unique global solution of the Camassa–Holm equation. The approach also provides a convergent, energy preserving nondissipative numerical method which is illustrated on several examples.

**Paper:**- Available as PDF (296 Kbytes), Postscript (1040 Kbytes) or gzipped PostScript (352 Kbytes; uncompress using gunzip).
**Author(s):**- Helge Holden, <holden@math.ntnu.no>
- Xavier Raynaud, <raynaud@math.ntnu.no>
**Publishing information:****Comments:****Submitted by:**- <raynaud@math.ntnu.no> January 13 2005.

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Conservation Laws Preprint Server <conservation@math.ntnu.no> 2005-01-21 15:49:09 UTC