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Global conservative multipeakon solutions of the Camassa-Holm equation. (English) Zbl 1128.65065
The authors show how to construct globally defined multipeakon solutions of the Camassa-Holm equation (the construction includes the case with peakon-antipeakon collisions). The solutions are conservative (the associated energy is constant for almost all times). They also construct a new set of ordinary differential equations to determine the multipeakons globally. The system remains globally well-defined. The presented methods can be used to derive numerical methods that converge to conservative solutions.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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