On the Cauchy problem for the modified Novikov equation with peakon solutions

A new nonlinear dispersive partial differential equation with cubic nonlinearity, which includes the famous Novikov equation as special case, is investigated. We first establish the local well-posedness in a range of the Besov spaces B-p,r(s), p,r is an element of [1, infinity], s > max{3/2, 1 + 1/p} but s not equal 2 + 1/p (which generalize the Sobolev spaces H-s), well-posedness in H-s with s > 3/2, is also established by applying Kato's semigroup theory. Then we give the precise blow-up scenario. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. Finally, we prove that peakon solutions to the equation are global weak solutions. (C) 2012 Elsevier Inc. All rights reserved.