Abstract
The negative order Camassa-Holm (CH) hierarchy consists of nonlinear evolution equations associated with the CH spectral problem. In this paper, we show that all the negative order CH equations admit peakon solutions; the Lax pair of theN-order CH equation given by the hierarchy is compatible with its peakon solutions. Special peakon-antipeakon solutions for equations of orders-3and-4are obtained. Indeed, forN≤-2, the peakons ofN-order CH equation can be constructed explicitly by the inverse scattering approach using Stieltjes continued fractions. The properties of peakons forN-order CH equation whenNis odd are much different from the CH peakons; we present the caseN=-3as an example.
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