Abstract
Recently, Novikov found a new integrable equation (we call it the Novikov equation in this paper), which has nonlinear terms that are cubic, rather than quadratic, and admits peaked soliton solutions (peakons). Firstly, we prove that the Cauchy problem for the Novikov equation is locally well-posed in the Besov spaces B-2,r(s) (which generalize the Sobolev spaces H-s) with the critical index s = 3/2. Then, well-posedness in H-s with s > 3/2, is also established by applying Kato's semigroup theory. Finally, we present two results on the persistence properties of the strong solution for the Novikov equation. (C) 2011 Elsevier Inc. All rights reserved.