Abstract
All nonlinear dispersive wave equations in the general class are known to possess multi-peakon weak solutions. A classification is presented for families of multi-peakon equations in this class that possess conserved momentum; conserved H1 norm of u; conserved H2 norm of u; conserved L2 norm of m; related conservation laws. The results yield, among others, two interesting wide families of equations: for which the H1 norm of u is conserved; for which the L2 norm of m is conserved. The overlap of these two families yields a singular equation which is nevertheless found to possess both smooth solitary wave solutions and peakon travelling wave solutions.
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