Derives multi-peakon dynamical system and proves local well-posedness in Besov spaces, blow-up criteria, global/blow-up conditions on initial data, and ill-posedness in B_{2,∞}^{3/2} for Camassa-Holm equations with quadratic nonlinearities.
Lundmark, Formation and dynamics of shock waves in the Degasperis–Procesi equation, Journal of Nonlinear Science, 17(3):169–198, 2007
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Peakon solutions and analytical properties for the Camassa-Holm type equations with quadratic nonlinearities
Derives multi-peakon dynamical system and proves local well-posedness in Besov spaces, blow-up criteria, global/blow-up conditions on initial data, and ill-posedness in B_{2,∞}^{3/2} for Camassa-Holm equations with quadratic nonlinearities.