AN ab-FAMILY OF EQUATIONS WITH PEAKON TRAVELING WAVES

Peakon traveling wave solutions, both on the line and on the circle, are derived for a novel ab-family of nonlocal evolution equations with cubic nonlinearities. At least two members of this ab-family, namely the Fokas-Olver-Rosenau-Qiao equation and the Novikov equation, are known to be integrable. Furthermore, a generalization of the ab-family with nonlinearities of order k is an element of N, k >= 2, is considered and its multi-peakon on the line is obtained.