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Numerical simulation of Camassa-Holm peakons by adaptive upwinding. (English) Zbl 1156.65313

Summary: The Camassa-Holm equation is a conservation law with a non-local flux that models shallow water waves and features soliton solutions with a corner at their crests, so-called peakons. In the present paper a finite-volume method is developed to simulate the dynamics of peakons. This conservative scheme is adaptive, high resolution and stable without any explicit introduction of artificial viscosity. A numerical simulation indicates that a certain plateau shaped travelling wave solution breaks up in time.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25 Solitary waves for incompressible inviscid fluids
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