Abstract
A two component generalization Camassa–Holm equation with peakon is proposed, which is associated with a 2 × 2 matrix spectral problem with two potentials. As its reduction, a new integrable peakon equation is derived. Then positive flows associated with the 2 × 2 matrix spectral problem are discussed, a new hierarchy of nonlinear evolution equations is obtained. Subsequently, N-peakon of the peakon equation are constructed and the dynamical system with which the N-peakon evolve is deduced. As an example, exact single peakon and 2-peakon are given and their figures are plotted. Moreover, infinitely many conserved quantities of the peakon equation are obtained.
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