Convergence of the dispersion Camassa-Holm N-Soliton

Abstract

In this paper, we show that the peakon (peaked soliton) solutions can be recovered from the smooth soliton solutions, in the sense that there exists a sequence of smooth N-soliton solutions of the dispersion Camassa-Holm equation converging to the N-peakon of the dispersionless Camassa-Holm equation uniformly with respect to the spatial variable x when the dispersion parameter tends to zero. The main tools are asymptotic analysis and determinant identities.