A convergent numerical scheme for the Camassa–Holm equation based on multipeakons
Helge Holden and Xavier Raynaud
The Camassa–Holm equation
enjoys special solutions of the form
denoted multipeakons, that interact in a way similar to that of solitons.
We show that given initial data
is a positive Radon measure,
one can construct a sequence of multipeakons that converges in
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.
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- Helge Holden,
- Xavier Raynaud,
- Publishing information:
- Submitted by:
January 13 2005.
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